Hot water and cold water switched in shower
I did this a while ago in my shower. I can't remember exactly, but that stem sticking out is part of a bigger cylinder/canister that fits inside of the big pipe. When I did it I worked the whole canister out of the pipe (it was stuck in there pretty good), took a look at it and played with it until I got the right rotation.

Like Daniel suggests, you want to make sure each limit of the movement is fully hot or fully cold. If you get it wrong you can miss the full range, or even have a dead spot in the middle with hot and cold on either side.

It looks like you have to take the front cover of that pipe of to get the canister out. Have fun.