The screws of the hinges on our kitchen cabinets are loosening in the frame and I'm not sure what's the best solution to fix this problem. Any suggestions/ideas?
Tighten the screws. If the screw holes are enlarged or degraded so that the screws no longer stay tight, withdraw the screws and coat the holes with a five-minute epoxy. This will firm them up. Apply some wax to the screws before re-inserting them or they will be permanently fixed.
Even easier than that is to fill the hole with wooden toothpicks and a little wood glue. White glue will work in a pinch. When the glue is dry, trim the toothpicks flush and reinstall the door.
I am also a fan of the toothpick trick. Quick easy way to give screws something to bite