Given the reaction agi(s) ↔ ag+(aq) + i-(aq) solution equilibrium is reached in the system when

Missing question:
1) the rate of dissolving reaches zero 
2) the rate of crystallization reaches zero 
3) the rate of dissolving is zero and the rate of crystallization is greater than zero.
4) both the rate of dissolving and the rate of crystallization are equal and greater than zero.

Answer is: 4) both the rate of dissolving and the rate of crystallization are equal and greater than zero.
Silver chloride (AgCl) dissolves and form silver and chlorine ions, in the same time silver and chlorine ions crystallizate and form solid salt silver chloride.
In equilibrium rates of dissolvinf and crysallization and concentration of ions do not change.