Step 1: Finding the hybridization of \([CoF_6]^{3-}\).
- The oxidation state of Co in \([CoF_6]^{3-}\) is:
\[
x + 6(-1) = -3 \Rightarrow x = +3
\]
- The electronic configuration of \( Co^{3+} \) is \( 3d^6 \). Step 2: Determining hybridization.
- Fluoride (\( F^- \)) is a weak ligand and does not cause pairing of \( d \)-electrons.
- Hence, Co uses \( sp^3d^2 \) hybridization, resulting in octahedral geometry. Step 3: Identifying the correct answer.
- Since \([CoF_6]^{3-}\) exhibits \( sp^3d^2 \) hybridization, the correct answer is (C).