It doesn't take much of a blow to break hinge screws out of a particleboard door. If the screws just stripped and pulled out cleanly, you could fill the hole with toothpicks and wood glue, then reinstall the screws. But if the surrounding particleboard has broken away, it's quicker to fill the void with gap-filling glue (Loctite Go2 Glue is one choice, and is available through our affiliation with Amazon.com).
Start by removing the hinge and preparing the damaged area (Photo 1). Apply petroleum jelly to the movable portions of the hinge to protect them from the glue. Then scuff the cup portion of the hinge with sandpaper where it will contact the adhesive. If you're using polyurethane adhesive, dampen the hinge with water to activate the glue. Apply glue to the damaged area and immediately install the hinge and screws (Photo 2). Secure the hinge with weights or clamps until the glue dries. Then reinstall the door.