Step 1: Understanding the Complex.
The complex is \( [Co(NH_3)_6]^{3+} \), and ammonia (NH\(_3\)) is a neutral ligand. The charge on the complex is +3, meaning the charge on the central metal ion \( Co^{3+} \) is +3.
Step 2: Determining Oxidation State and Unpaired Electrons.
For \( Co^{3+} \), the oxidation state of Co is +3. In a \( d^6 \) configuration for \( Co^{3+} \), the number of unpaired electrons is 3.
Step 3: Conclusion.
The correct answer is (B) \( x = 3, y = 3 \).