My mother-in-law brought us a very nice cabinet that weighs 30 pounds and is 20"W x 32"H x 4"D. She got it from her parents, and we suspect it was sitting on top of another piece of furniture that we don't have -- there's a "slot" on the bottom of the cabinet that is about 16"x1.5"x1.5" and has four holes on the four sides of the slot that are each about half an inch in diameter and half an inch deep.
I'm picturing that it sat on a credenza that was fitted to this piece, and perhaps it was anchored to the wall at the top through a couple of metal brackets on the top back of the unit that aren't substantial enough to support it at all but are probably enough to keep it near the wall.
Any thoughts on how to hang this on drywall? My idea is a couple of L brackets in studs with a piece of wood attached to the Ls that is fitted to match the bottom and then stained to match the cabinet, although I'm not really sure how to create or acquire that piece of wood.
As recommended by r13, here are some pictures I've added. This would be going onto drywall.