Remove the damaged door from the cabinet by removing the screws that secure the door hinges to the cabinets with a screwdriver. If the door hinges are held in place with a vertical pin, drive the pin upward with a screwdriver and a hammer.
Position the door on a flat surface.
Wash the front of the cabinet with a mild detergent, then rise the detergent off the door with clean water and a sponge.
Scrape away any loose paint surrounding the cracks with a putty knife.
Fill the cracks with a latex wood patch product using the putty knife as an applicator. Spread the patch product across the surface while pressing the material into the door. Scrape the excess material off the door with the putty knife before the material dries.
Allow the wood patch material to dry.
Sand the entire surface of the door with fine-grade sandpaper. It is not necessary to remove the existing paint. The purpose here is to rough the surface slightly to give new paint something to adhere to.
Wipe down the cabinet with a tack rag to remove the sanding residue.
Apply a fast-drying oil-based primer across the patch area with a paintbrush. It is not necessary to prime the undamaged portions of the door.
Paint the door with a 2-inch trim brush. Paint the center section of a door with recessed panels before painting the horizontal tails and vertical stiles.
Allow the paint to dry, then apply a second coat of paint if necessary. If applying a second coat, sand the first coat slightly to rough its surface, then wipe the door down with the tack cloth before painting.
Apply a single coat of clear wood sealer across any unpainted surfaces of the door with the paintbrush to prevent moisture from penetrating the wood.