This is the 12415th most frequent Polish word.
mężczyznom
The word "mężczyznom" means "to men" in English.
The word 'mężczyznom' is the dative form (third case) of the noun 'mężczyzna,' which means 'man.' It shows whom the waiter directed the action of giving the menu.
W restauracji kelner podał menu tylko mężczyznom.
In the restaurant, the waiter handed the menu only to the men.
Here, 'mężczyznom' is again in the dative form and indicates the recipients of the cheering, specifying for whom the support was meant.
Na zawodach sportowych kibice dopingowali mężczyznom startującym w biegu.
At the sports event, the fans were cheering for the men participating in the run.
In this context, 'mężczyznom' refers to the indirect object of the verb 'udzielił,' meaning 'taught,' indicating to whom the advice was given.