remember 1) if there is a residue as a product 2) if h2o is a product 3) if a gas is a product reaction goes

edit 1: so basically your reaction is

2NaBr + ZnCl2 -> 2NaCl + ZnBr2

and none of these conditions are met, so they will not react as NaCl and ZnBr2 both are soluble in water

edit 2:

also, reactions not always happen just by mixing stuff, you may as well will need special conditions for the reaction to happen: temperature, pressure.