“This article got me to thinking about those who say the Bible states that God only took 6,000 years before the creation of Adam and Eve, the first man and woman, who were created about 6,000 years ago”
Are you saying these people think the world is 12,000 years old? 6,000 from Creation to the first man and woman, then another 6,000 to the present?
I don’t know of any Christian denomination which believes that.
“science book”
The passage quoted does not try to use the Bible as a science book.
Besides, science is just one more way of studying what God is done, and how He has set things up.
There are a couple of posts here that infers rather strongly that there are those who believe the first part of Genesis should be used as a science book.
I know of denominations that believe that each day of the creation was 1000 years and that it’s been 6000 years since the creation of Adam and Eve and they are rather emphatic about that.