Open the cabinet door and hold it with one hand. Remove the screws that secure the hinge to the inside of the cabinet with a Phillips head screwdriver. Repeat for both hinges.
Place the cabinet door face-down on a flat surface. Remove the screws that secure the hinge to the door with the Phillips head screwdriver.
Squeeze wood glue into the screw holes on the cabinet door and the inside of the cabinet. Stuff toothpicks into the holes. Typically, you can insert two toothpicks into each hole.
Take one of the hinges to the hardware store to purchase replacement hinges while the glue dries in the screw holes. You need to get 1/4-inch inset hinges of the same size cup as the current hinges. This will ensure that the new hinges fit the cup holes in the door.
Cut the toothpicks flush to the surface of the doors and inside of the cabinet with a utility knife once the wood glue dries completely. Sand the area with 100-grit sandpaper until the top of the toothpicks is flush with the cabinet surface.
Insert the cup of the inset hinge into the cup hole on the cabinet door. Secure the hinge with the retaining screws. The toothpicks and glue act as new material for the screws to dig into and hold.
Position the cabinet door in place and line up the hinges with the toothpick-filled holes. Secure the hinge to the inside of the cabinet with the securing screws. Repeat the process for all of the cabinet doors.