In Hebrews 9:26For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself.
See All... Paul (or whoever may be writing) said that Christ had appeared "once "IN THE END OF THE WORLD" to atone for sins. How can it be the "end of the world" when it happened almost 2,000 years ago (considering that this world is only 6,000 plus years old)?

This is an excellent question. From our standpoint, especially for those of us who are looking for the end of the world, placing the end of the world almost 2,000 ago does seem odd. Yet, this is what Hebrews 9:26For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself.
See All... does. Christ "appeared to put away sin by the sacrifice of himself" in "the end of the world." Obviously, God does not look at time the same way we do. There must be some special meaning to this verse. However, we need to look at several aspects of Bible teaching in order to understand this fully.

The New Testament epistles have several references to their time as the last times. We ave already seen that the first coming of Christ as the suffering Saviour was at the end of the world. 1 Corinthians 10:11Now all these things happened unto them for ensamples: and they are written for our admonition, upon whom the ends of the world are come.
See All... tells us that what happened to the Israelites in the past were ensamples for us "upon whom the ends of the world are come." That is, we who live in this age of grace are experiencing the ends of the world. Other verses add to this idea.

Hebrews 1:2Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;
See All... says that God has "in these last days spoken unto us by his Son." This squarely puts us in the last days. In 2 Timothy 3:1This know also, that in the last days perilous times shall come.
See All... Paul seems to prophecy, "This know also, that in the last days perilous times shall come." Yet, as the passage is read in full, it seems that he is placing us in these "last days." When referring to those having a form of godliness while denying its power, he adds, "of this sort are they which creep into houses" (2 Timothy 3:6For of this sort are they which creep into houses, and lead captive silly women laden with sins, led away with divers lusts,
See All...). In speaking of those who are ever learning but not able to come to the knowledge of the truth, he says, "so do these also resist the truth: men of corrupt minds, reprobate concerning the faith" (2 Timothy 3:8Now as Jannes and Jambres withstood Moses, so do these also resist the truth: men of corrupt minds, reprobate concerning the faith.
See All...). Evidently, Paul places his own time in the last days and believes that the characteristics of the last days will continually get worse.

1 Peter 1:20Who verily was foreordained before the foundation of the world, but was manifest in these last times for you,
See All... tells how Christ "was manifest in these last times for you." 1 John 2:18Little children, it is the last time: and as ye have heard that antichrist shall come, even now are there many antichrists; whereby we know that it is the last time.
See All... declares, "even now are there many antichrists; whereby we know that it is the last time." In context, the antichrists are those who deny that Christ was fully God and fully man. We certainly still have these antichrists today. They point to the soon coming of the Antichrist.

Consider this passage in 1 Corinthians:

1 Corinthians 7:29But this I say, brethren, the time is short: it remaineth, that both they that have wives be as though they had none;
See All... But this I say, brethren, the time is short: it remaineth, that both they that have wives be as though they had none; 30 And they that weep, as though they wept not; and they that rejoice, as though they rejoiced not; and they that buy, as though they possessed not;  31 And they that use this world, as not abusing it: for the fashion of this world passeth away.

Paul says that "the time is short" and that "the fashion of this world passeth away." In Philippians 4:5
See All..., he states, "The Lord is at hand." James 5:8Be ye also patient; stablish your hearts: for the coming of the Lord draweth nigh.
See All... warns, "for the coming of the Lord draweth nigh." Romans 13:11-12 [11] And that, knowing the time, that now it is high time to awake out of sleep: for now is our salvation nearer than when we believed. [12] The night is far spent, the day is at hand: let us therefore cast off the works of darkness, and let us put on the armour of light.
See All... declares, "for now is our salvation nearer than when we believed. The night is far spent, the day is at hand." Finally, 1 Peter 4:7But the end of all things is at hand: be ye therefore sober, and watch unto prayer.
See All... tells us, "But the end of all things is at hand: be ye therefore sober, and watch unto prayer." Both the epistles of Paul and the epistles commonly called the general epistles tell us that we are in the last days and the coming of the Lord is at hand.

What then defines the end of the world or the last days in God's view? Hebrews 9:26For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself.
See All..., the verse about which you asked, clearly defines this time. Hebrews 9:26For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself.
See All... states, "but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself." The end of the world is defined as that time when Jesus comes to make a sacrifice for sins. It is the first coming of the Lord Jesus. This agrees with other scriptures.

Jacob's prophecy in Genesis 49:10The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be.
See All... states, "The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be." Shiloh is the Messiah--the Lord Jesus Christ. All Jews understood that the end of the world was marked by the coming of their Messiah. The problem is that the Jews did not make a distinction between the first and second coming of Christ. The truth is, neither did the Old Testament. Isaiah 9:6For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.
See All... says, "For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace." Is this talking of the first coming or the second coming? We know that the child was born at the time of the first coming. But the government will not be place on His shoulders until He comes again. The two are looked at as one.

The problem from the point of our understanding is the two comings and the (now) long time between them. The Bible see them as part of one event. They are the coming of the Messiah in order to set up His kingdom on earth. However, because the Jews initially rejected Him and the Gentiles were given a chance to receive Him as their Lord and Saviour, the time has drawn out. However, from God's vantage point, it is all the last days and the end of the world. The entire Old Testament prophetic message pointed to the coming of the Jewish Messiah. When Jesus came, His coming marked the fulfillment of this long held expectation. The end of the world had come. And though to us the wait for the second coming has seemed to be long, the Lord is at hand and ready to show up at any moment.

So, what about those who mock the seemingly delayed coming of Christ? The Bible has the answer for them as well. Consider this passage:

2 Peter 3:3Knowing this first, that there shall come in the last days scoffers, walking after their own lusts,
See All... Knowing this first, that there shall come in the last days scoffers, walking after their own lusts,  4 And saying, Where is the promise of his coming? for since the fathers fell asleep, all things continue as they were from the beginning of the creation.  5 For this they willingly are ignorant of, that by the word of God the heavens were of old, and the earth standing out of the water and in the water:  6 Whereby the world that then was, being overflowed with water, perished:  7 But the heavens and the earth, which are now, by the same word are kept in store, reserved unto fire against the day of judgment and perdition of ungodly men.

This passage recognizes that many will give up hope and turn from the promises of the Lord. But He will still come. I cannot say when but I know that the time is at hand. I know that my salvation is nearer than when I first believed. God's timing is not as ours. Since time means nothing to Him (in the way we are controlled by it), He figures by major events. When Jesus came, it marked the end of the world. And although the final page has still not been turned 2,000 years later, I know that it is all settled and that I live in the end days looking and longing for the return of my wonderful Saviour.