Answer:
Empirical evidence is evidence that is verified by observation or experience, rather than logic or theory.
Then an explanation is based in on empirical evidence is an explanation that uses a fact that was seen or experienced.
The case here:
"Ancient text reveals that the universe is about 6000 years old"
Is not empirical, because there is no observation or experience here, this is only a book that says the opinion of who wrote it.
An example of an empirical explanation would be:
"The universe is at least X years old because we can see remanents that are X years old"
