What is the product for the reactant NH4OH+Br?

NH4OH = NH4(+) + OH(-)

Br? Is this Bromide (Br-) or Bromine, Br2? If it's bromide, as I suspect, then you're missing a counter ion (for example, Na+ from NaBr, K+ from KBr, etc).

If it's bromide, you can get an equilibrium

NH4OH + XBr = NH4Br + XOH

Simply break the compounds down into their ions and then intermix the ions. Unless there's something "driving" the reaction to one side or another (like precipitation of XOH if X were something like Ca), then all species would be in equilibrium.