There are some parts not shown in the picture: 1. ~ 1/2" round, flexible gasket-like thing (nylon/neoprene maybe), with a couple small holes through it. The flexible gasket-like thing fits down in that cavity in the body of the petcock (on the right). It functions as the seal between the moving face of the handle parts (on the left), and the non-moving face in the cavity. When the petcock leaks, this is usually the part that fails - due to wear. If yours is intact, take care not to damage it in removal, dis-assembly, cleaning, and reassembly. Re-install it with the flat face out, toward you in the picture, with the gasket holes positioned directly over the holes in the bottom of the cavity. If your gasket-like thing is shot or you damage it, good luck. Seems like I recently saw one on offer for pennies at a moped parts website... in Europe. Otherwise, time to buy a new petcock. 2. The hex-shaped section that appears in the picture to be one piece with the body of the petcock, is actually a separate part, i.e., a threaded sleeve. Every one of these I've seen unscrews from the body of the petcock and removes for cleaning. Maybe not all though. Also, most petcocks have a 1' to 5" long, 1/4" round, fine-mesh tube, the primary fuel filter, extending out of the sleeve. The filter is one piece with the petcock. Be careful with the filter in dis-assembly, cleaning, reassembly. Whether or not a fuel filter is attached, down inside the sleeve is a non-metallic washer (not shown). Don't lose it.
Finally, note the little tit on the black washer on the petcock handle. During reassembly, fit the tit in the slot at the bottom of the body of the petcock to line it up properly inside, then screw on the handle.