What can be wrong when a Mitsubishi GTO won't engage in reverse?

a common problem is a water coolant pipe or front air intake pipe obstructing the gear change lever on the top of the gearbox. a pain in the arse but easier to fix than a broken syncro.

if you can get the car to reverse by holding the gearstick in reverse than this could be your problem. if its grinding than you have a damaged syncro, or your clutch doesnt dis-engage properly