plumbing for shower and commode in upstairs 2 x 6 floor

I think she means 2x6 floor joists were used maybe?

Why was the floor framed with 2x6's?!?

If that meets code (and I'd be surprised if it did), you have a couple of options:

1) Change it from a shower to a tub. A shower requires a 2" drain while a tub only needs an 1 1/2" drain - assuming you're within so many feet between the trap and the vent (in my state, that's 5 feet, but check your local codes). An 1 1/2" ptrap will fit within 2 x 6 framing.

2) If you have the height below, drop the ceiling to give you a couple more inches. Strapping nailed to the bottoms of those joists will give you an extra 3/4" to play with - maybe double, or triple strap it if you have to.

Hopefully, the toilet is close enough to a partition below that you don't have to run very far. Within a 2x6 floor structure, the closet bend will already be at, or below the bottom of the joist even when it's pushed up as high as possible. Then the horizontal drain needs to have 1/4" pitch until it drops to vertical. That strapping (mentioned above) will get you (hopefully) a maximum 3 foot run.

And finally, you certainly can't drill a 3 5/8" (OD) hole through a 2x6, so unless the toilet drain runs straight down between two joists and immediately down a "wet wall", you won't be able to do it.