The correct preposition here is "from" because "protruding from the wall" correctly describes an object extending outward or projecting from something.
"Below" would indicate a position beneath the wall, but the context describes projection, not placement under.
"About" and "underneath" do not appropriately fit the context of protruding, which specifically refers to something coming out or extending from the surface.
Thus, the correct preposition is "from", making the sentence "He hung his coat on a nail protruding from the wall."