Step 1: Identify the type of complex.
The complex is \([\text{Co(NH}_3)_6]\text{Cl}_3\), a typical hexamminecobalt(III) chloride. When dissolved, the cation is \([\text{Co(NH}_3)_6]^{3+}\) and there are three Cl\(^-\) ions.
Step 2: Reaction with AgNO\(_3\).
Each Cl\(^-\) reacts with Ag\(^+\) to form AgCl:
\[
3\text{Cl}^- + 3\text{Ag}^+ \rightarrow 3\text{AgCl}
\]
Thus, the number of ions produced in solution = 1 cation + 3 anions = 4 ions.
Step 3: Conductivity explanation.
Conductivity of solution depends on total number of ions. Here, \([\text{Co(NH}_3)_6]^{3+}\) + 3 Cl\(^-\) = 4 ions per mole of complex.
Step 4: Final conclusion.
Hence, the molar conductivity corresponds to:
\[
\boxed{4\, \text{ions mol}^{-1}}
\]