Its a bit awkward, this one as your cupboards will be made from a chipboard or MDF material that has little strength....anyway you can either move the hinge down a little and replace it, or more likely, glue some matchsticks into the hole thats left - use a PVA woodwork glue, pack the matchsticks in tight to fill the hole and be patient, giving the glue plenty of time to dry.
John, July 2009