it might be a chore to get it out of there but probably a drill and e-z-out will get it, maybe from the right side for easier access if there is more room , it may just screw all the way through.
If it is a 6 mm it is only about 1/4 inch diameter so be careful tightening the new one or the head may snap off that one too. I thought it looked like an 8 mm size by the photo, maybe not.