Nothing is really 'broken', it's just that the prongs of the hook/clamp affair came out of one of the hardwood jaws.
I'll put it back together with CA adhesive, but I'll add a little touch that will make the glue-join even more secure. I'll file a few shallow notches in the prongs, to give the adhesive some 'tooth', like so.
Here's the hanger reassembled with CA adhesive.
That should stay together approximately forever.
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