What mass of ammonium hydroxide is needed to react completely with 75.0g of copper(II) nitrate in a double displacement reaction?

Of course. The formula is absolutely necessary to the working of the problem.
2 NH4OH + Cu(NO3)2 → Cu(OH)2 + 2 NH4NO3

(75.0 g Cu(NO3)2) / (187.5558 g Cu(NO3)2/mol) x
(2 mol NH4OH / 1 mol Cu(NO3)2) x (35.0458 g NH4OH/mol) =
28.0 g NH4OH