I have a load bearing wall and I want to remove the wall.It is a 12 foot opening with a second story on top. I know I have to replace the wall with a beam. But I don't want the beam to come down to far. What is the smallest that I can make my beam. I was going to use a 2x10. Can I go smaller 2x8 or 2x6?

No body in their right mind would size a beam from the information that was given.

If this is "simple" construction then the appropriate codes books will have tables in them.

But those are the only size that can be used. And there are alternate materials such as egineered wood beams, steel, and a fitch beam.

And you have other issues such as where the point loads from the support studs land.