I can help
Let me read the question abit closer
I have attached a guide that covers all of the limit for notching and boring.
The short answer is no you can not bore that large of a hole through a 2x6
You are limited to 1.5" in a 2"x6" joist
Are you still there?
Sorry your maximum bore hole diameter in a 2x6 is d/3 or 1.83"