Repair Faux Wood Grain on Cabinetry
Repairing this type of material is difficult, although I have seen it done.  It is an art project of matching paint colors and drawing in the wood grain.  I doubt it will hold up though.  Covering it up is your best option and there are several ways to do it.

1 - I think your best bet is to find a cabinet refacing supplier.  There are many on the internet and you should be able to find an end skin.  This is either a thin sheet of plywood or veneer and many are self adhesive. In cabinet refacing, they cover the outside surfaces of a cabinet and replace the doors so they have a lot of color and wood options.

2 - You can buy what is essentially wood grain contact paper and cover it up.  Be sure that surface is as clean as possible before applying the new contact paper.

3 - I see a small strip of wood at the bottom.  I would have to see what the whole cabinet looks like, but you may be able to take that off and replace it with a wider strip of wood if the damage is confined to the lower part of the cabinet as it appears in this picture.

4 - You can go the a local wood store and buy veneer or thin plywood and stain it to match.

Good Luck!