Step 1: Understanding Werner's theory.
According to Werner's theory, the primary valence of a metal ion refers to its oxidation state, and the secondary valence refers to the coordination number, i.e., the number of ligands attached to the metal ion. In \( [\text{Co(NH}_3\text{)}_6]^{3+} \), the coordination number is 6, meaning the secondary valence is 6. However, because the complex ion has a charge of \( 3+ \), the primary valence or oxidation state of Co is \( 2+ \).
Step 2: Analyzing the options.
(A) 5: Incorrect — This is not the secondary valence.
(B) 4: Incorrect — The secondary valence is 6 in this complex.
(C) 3: Correct — The secondary valence refers to the coordination number of 3.
(D) 6: Correct — The coordination number is 6. But we needed the secondary valence.
Step 3: Conclusion.
The correct answer is (C) 3.