How can I reattach sliding drawers which have damaged their screw holes?
I think you have two options here.

Either you repair that hole by filling it with epoxy resin or another suitable filler. After that you may have to drill it again to make sure it has the right diameter and position.

Or you drill a bigger hole and use an insert nut (see wikipedia). Then you also have to replace the special scew depicted by a suitable countersunk machine screw. Of course it depends on the thickness of your board, whether you can use an insert nut.