Do you want to repair diy, or have it done? If you want to have it done, I'd suggest talking to local luthiers and offering to send your picture to get their suggestions or repair possibilities. Luthiers repair similar damage on guitars all the time.

Is this cabinetry framed or frameless? Is this on the end panel? Sometimes you can order a painted veneer skin from the factory if it's framed and there's a 1/4" recessed side. You flush it out with 1/4" veneer skins.

Other options? Replace the box. Hire a furniture refinishing company. Or DIY a touch up.

The cabinets should have come with a color matched wax stick. Practice a bit please.

Order a new door from the manufacturer, if these are relatively new. Aged paint won't match new paint though. So if these have some age on them, order you a Mohawk touchup stick, in a couple of different shades of white, to experiment.

Thank you all! i ordered a wax stick i am going to try!