The octahedral complex [CoF₆]³⁻ is paramagnetic…

Step 1. The ion. $\text{Co}^{3+}$ has $27 - 3 = 24$ electrons, so $3d^6$.

Step 2. The fluoride complex. $\text{F}^-$ is weak and does not force pairing. The six electrons fill the five 3d orbitals as one pair and four single electrons. No 3d orbital is empty, so the ion uses the 4d orbitals: $sp^3d^2$, an outer orbital complex. Four electrons are unpaired.

Step 3. The ammonia complex. $\text{NH}_3$ is strong. The six electrons pair up in three 3d orbitals. Two 3d orbitals are empty and join the 4s and the three 4p orbitals: $d^2sp^3$, an inner orbital complex. No electron is unpaired.

Step 4. The moment. For four unpaired electrons, $\mu = \sqrt{4 \times 6} = 4.90\ \text{BM}$.