Why Agcl is soluble in NH3
AgCl(s) <--> Ag+(aq) + Cl-(aq) --(1)
Since AgCl is insoluble, the equilibrium lies to the left.
In aq NH3, :NH3 acts as a ligand and forms a complex with Ag+ :
Ag+(aq) + 2NH3(aq) <-->[Ag(NH3)2]+ (aq) --(2)
Reaction(2) lowers the concentration of Ag+ and shifts the equilibrium of (1) to the left, dissolving AgCl.