mouth hole vs hole

mouth hole and hole both are nouns.

Word	Noun	Adjective	Verb	Adverb
mouth hole	Yes	No	No	No
hole	Yes	No	Yes	No

As nouns, hole is a hypernym of mouth hole; that is, hole is a word with a broader meaning than mouth hole:

mouth hole (noun)	hole (noun)
a hole (as in a ski mask) for the mouth	an opening deliberately made in or through something
	one playing period (from tee to green) on a golf course
	informal terms for the mouth
	an opening into or through something
	a depression hollowed out of solid matter
	an unoccupied space
	informal terms for a difficult situation
	a fault

mouth hole (verb)	hole (verb)
	make holes in
	hit the ball into the hole