Can't remove 6mm hex pedal
Stuck 6mm-only pedals can be a very tough situation, unfortunately.

Presuming an aluminum crank, heat, either from a heat gun or torch, is a method some mechanics go to quickly here. The idea is the different materials expanding and contracting at different rates thermally shocks the corrosion free. Personally I'm squeamish about this and never do it on other people's bikes, out of fear of metallurgical consequences (ruining the heat treatment etc) that might not be obvious. That said, it's a pretty common practice and probably unlikely to bite you in any meaningful way. 

I tend to soak it in some kind of penetrating oil for at least a day. Lately I've been using Finish Line Chill Zone, which thermally shocks it using cold. I put a plastic bag around the pedal, rubber band it around the crank, and position it so the threaded part is being bathed in oil. This also contains the mess and smell, which is nice.

To do the actual breaking free, what I do if possible is clamp a 6 poking straight up in the vise, put the crank on top of that, and try to find some way of applying massive leverage to the crank, usually via a Park FFS. I've also clamped the cranks using smooth jaws and rags, but this is pretty likely to do some kind of marring to the cranks anyway given all the force involved.