If the Earth is 6,000 years old, why can we see stars from millions of light-years away

This is something that someone else pointed out in answer to a question, and I thought it was a good point. There are many reasons why the assumption that Earth is 6,000 years old is erroneous: man-made inventions came from long before then; history and geological samples talk of human civilisations waaay before then; the Bible clearly uses a different calendar method to us (Adam, for instance, was over 900 years old according to the Bible, which doesn't match up to today's understanding of a 'year'.) The list goes on.

Why are there still some people who believe that the Earth is 6,000 years old? Is The Bible says so equivalent to There are thousands of peer-reviewed theses and papers by reputable Ph.D-winning scientists that prove so?

I won't say it isn't a problem, but it isn't a problem for me after hearing a PhD explain that local time, gravity, and relative time paradox combine to reflect that 'God stretched the heavens' sometime after day 4 of creation week. Perhaps this is a cop-out for a scientist, but it fits within the creationist framework.

A creationist would proceed to deny either the distance of stars or the speed of light, perhaps invoking Satan's tricks as an excuse.

If you are only 20 years old, why are you able to read a book that was written 2000 years ago?

Light years is an expression of distance, not time.
The Earth is also 4 billion years old - not 6000

Good for you, use that brain, question things which don't make sense.

The assumption that the Earth is 6000 years old comes from "Chronologies" proposed by English philosophers from the 17th century that included Isaac Newton and James Ussher.

Chronologies were common in those days. The Church was flooded by proposals from various people, some more serious than others. By the time they got the one by Ussher (proposing that Earth was created in 4004 BC) they had already received evidence - from the region we now call the Middle East - that Earth was already older than that by at least a thousand years.