This is the 347th most frequent Polish word.
mężczyzny
The word "mężczyzny" in Polish means "of a man" or "man's" (genitive singular form of "mężczyzna").
Here, 'mężczyzny' is used in the genitive case to denote possession.
To jest dom tego mężczyzny.
This is that man's house.
In this example, 'mężczyzny' is again in the genitive case, here used after the preposition 'do' to show possession.
Samochód należy do mężczyzny.
The car belongs to the man.
Here, 'mężczyzny' is in the genitive case used with negation of a verb that would otherwise take the accusative case in a positive sentence.