Christians who use the Bible as a measuring stick for time come up with the number 6,000 for the age of the earth.  They use the genealogies of the Bible as a benchmark for the age of earth back to Adam.  They take the number of FATHERS times 60 or 70 years of age (pre-Noah people get longer dates) and back that up to the first man ADAM plus 6 days.  Not very scientific.

Some other problems....

Genealogies in the Bible were not recorded in accurate, step-by-step lineages.  Some generations were skipped, jumping to grandfathers or great-grandfathers.  Matthew manipulated his genealogy of Jesus to make a perfect 14-14-14 (or 7x2, "double perfection"), missing many generations so he can communicate the perfection of Jesus coming into the world.

The other problem is Carbon-14.  Are we absolutely sure that it is an accurate measurement to date ancient objects?  Do we have anything from 65 million years ago that we can use as a comparison to the data or do we just assume it's 65 million years old?  If someone told me a coin was from 1930 just because it looked like a coin from 1930, I could pull out a coin from 1930 whose date has been verified to compare it.  We have nothing from 65 million years ago to prove that date.

Some people put their faith in Carbon-14 like others put their faith in the Bible.  It's a blind trust without all the facts.

Since we cannot prove the earth was 65 million years old by science or 6,000 years old from the Bible, maybe the two meet somewhere in the middle.

The argument over the age of the earth is not a Christian's responsibility to get right.  We don't have to live or die on this mountain.  God will not ask us the age of the earth to allow us permission to enter heaven.  The Bible wasn't given to us so we could know the age of the earth.  It was given to us so we would know WHO created the earth.