But in Spanish if you can't hear what someone is saying you can say "¡No oigo!" which literally means "I don't hear!" but no one would ever say that. You'd say "I can't hear!" I think "The man can't hear" is a valid translation.
Two translations for this sentence is: The man does not hear. OR The man does not listen. But what if I wanted to say a specific one? Like if I was trying to say "The man does not hear" someone else might interpret as "The man does not listen."