1. He had his nosebone broken.
2.He had his nose bone broken.
3. He had his nasal bone broken.
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Which one is right? Nose bone or nasal bone?
"He had..." implies that he got someone else to break his nose for him! I doubt that's what you mean.
Also "nasal bone" is the correct term.
So here are some possibilities for rephrasing:
His nose was broken in the accident.
His nasal bone was broken in the accident.
He broke his nose while playing baseball.
He broke his nasal bone while playing basketball.