The word equation for the reaction between ammonium sulfate and sodium hydroxide is:
One mole of aqueous ammonium sulfate plus two moles of aqueous sodium hydroxide produce one mole of aqueous sodium sulfate plus two moles of ammonia gas plus two moles of liquid water.
The balanced chemical equation for this reaction is:
Since only the ammonium and hydroxide ions are interacting, the ion-equation would be:
The sulfate and sodium ions are "spectator" ions: they don't change.
The reaction above is not one-way. Part of the ammonia dissolves quite well in water, and forms an equilibrium with the ammonium and hydroxide ions: