The Bible seems to support man being around for 6000 years, with a total repopulation after the second world-wide flood with Noah 5000 years ago. But I don’t see the Bible supporting the idea that the earth itself is 6000 years old. Who knows who long the earth was around before the first recorded world-wide flood in Genesis 1:2?
James Ussher did a seminal work on this and came to the 6,000 year conclusion.
A running theory of mine is the duration of time in Eden is what is in question. I believe the dating of Adam's age came after the fall and that he and Eve had many, many children during their time in Eden. This is evidenced by Cain marrying in the land of Nod, east of Eden where there were presumably a good many people (offspring of Adam and Eve) where Cain built a city. Time, IMHO began after the fall and is thus recorded.
Careful now, evolutionary creationism is to be ridiculed by both sides, as the Creationist KNOW the history of the Word of God and the Evolutionists KNOW their theory is fact.