My college professor claims that the universe is 14 billion years old, but I was told that the Bible says 6,500 years old. Where does the Bible get that age?
Yes, the Bible does indeed make the claim that God created the earth, planets and all the stars 6,500 years ago. The Bible makes that claim historically; in Luke 3:23-28 there is a genealogy from Jesus back to Adam and scholars have dated that time at 4,500 years. We know that Jesus lived 2,000 years ago. Add up the numbers and you get 6,500 years.
There are a lot of people who trust what they think is science, and put the date at billions of years. The problem is that these people are giving science power of knowing the past, an ability it does not have. We need to understand that what we can learn from the scientific method is limited. Science is observable, testable and repeatable. Science can give us weak evidence that can point to a billion year old universe, but even that evidence is observable in the present. But that evidence can only bring the idea or thought of a billion year old universe as a theory, not as a fact based on observational science.
When you are seeking knowledge from the past, you need to use the method of history. History is learning information from the past based on written or oral testimony. The only problem with this method is the trust one has in the testimony. In the case with the age of the universe we have someone who was there and one we can trust, that person is God. He has documented how He created, how long He took to create, and how long ago this took place. God gave us the Bible so that we can know.
For the word of the Lord is right and true; He is faithful in all He does.