Please explain something for me.
You are building a porch that is 12' wide and 6' out, or the other way around?
You have chosen not to build a shed roof and you have a 2'rise and about a 7' run from peek to wall, (not including an overhang).
I would cut in some wind bracing in the walls and I think that 2 X 8's would be fine if the only load is the roof.
I have no idea where you are located and if you have snow loads to deal with and such.
When you apply for your Building Permit, your Building Inspector will tell you, after reviewing your plans, what is required.
I prefer to over build, (more power), for the future.
© 2017 Renovate Your World LLC