Three sets of wires for two switches in bathroom
I'm guessing the black from the light is always hot. So take that hot black and connect it to the black wire for the light in the other room. To that same connection, connect a 6" pigtail and the other end of the pigtail to the common terminal of your double toggle. The common terminal is probably the black screw but verify that with the switch diagram. Take the red from the light and hook it to the top switch terminal, usually a brass screw and hook the black from the fan to the bottom switch terminal, also usually a brass screw. Connect all your white wires together. Good luck and stay safe out there.