AgCl is soluble in ${\mathrm{NH}}_4\mathrm{OH}$ solution. The solubility is due to the formation of:

AgCl is soluble in  due to the formation of ${\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]}^{+}$

Ammonium Hydroxide is ammonia dissolved in water. When AgCl is introduced, it combines with ammonia to form ${\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]}^{+}$, also known as Diamine silver chloride, which is water soluble. As a result, AgCl is soluble in Ammonium Hydroxide but insoluble in water.