In this case, CoCl\(_3\)·4NH\(_3\) represents a coordination compound with cobalt as the central metal ion. The primary valency of the metal ion is given by the chloride ions (Cl\(^-\)), which are directly bonded to the metal ion. Since there are three chloride ions, the primary valency of Co is 3.
The secondary valency is the number of coordinate bonds that the metal ion forms with other ligands, which are the ammonia molecules (NH\(_3\)) in this case. Since the compound has 4 NH\(_3\) molecules, the secondary valency of Co is 6 (3 from Cl\(^-\) and 3 from NH\(_3\)).
The formation of AgCl upon addition of AgNO\(_3\) indicates that the chloride ions are in the primary coordination sphere, confirming that the secondary valency is 6.