It won't work like that. To use N channel mosfets on the high side you need a special driver to lift the gates above the 6v rail.
Look for a design with P Channel mosfets on the the high side or look for a ready made H-Bridge board.
375mA is not much current so you could use tiny relays that just barely make a small click noise if you put your ear right next to it but it's up to you.
Thanks, but isn't there something I need to change so it will work because I already have these Mosfets at home or won't it work because of how Mosfets work?
I planned to build a fake perpetuum mobile in form of a piston. I want to have a electromagnet to push and pull on a Neodymium magnet, so the piston moves.