Sand away the area where the slat attaches to the door, as well as any area where there are cracks and breaks in the slat itself. This removes any splinters and smooths away imperfections.
Wipe away the sandpaper dust and any other particles, both on the slat itself and on the door where the slat attaches.
Reattach the slat to the door in the same position it was before it broke. Put wood glue on the slat, and hold it in place until the glue achieves a hold. Then allow the glue to fully dry. To make the job easier, choose a wood glue that comes in a bottle with a thin applicator tip.
Fill in any cracks in the slat itself with wood putty and apply a small amount of putty to the area where the slat meets the rest of the door. If your door is not painted, use a putty that most closely matches the natural color of the door's wood.
Sand away areas where you applied the wood putty to achieve a smooth finish. Use a rag to wipe away any sandpaper dust.
Prime and paint the entire door or apply a stain. Allow the paint or stain to dry fully before opening or closing your bifold closet doors.