Dear student,
The reaction is as follows:
CH3COOH+NH4OH→CH3COONH4+H2O.
It is a simple acid-base reaction.Ammonium Hydroxide(NH4OH) and acetic acid(CH3COOH) have both H+ and OH- ions but in their aqueous state.Ammonium hydroxide liberates OH- ions in the solution as H+ ions remain attached to Nitrogen atom forming NH4+whereas, acetic acid liberates H+ ions in the soluiton .which makes it acidic and ammonium hydroxide as a base.
Regards