Three octahedral complexes are [V(H₂O)₆]³⁺, [Cr(NH₃)₆]³⁺ and [Mn(H₂O)₆]²⁺…

Step 1. 3d electrons. $\text{V}^{3+}$ has $23 - 3 = 20$ electrons, so $3d^2$. $\text{Cr}^{3+}$ has $24 - 3 = 21$ electrons, so $3d^3$. $\text{Mn}^{2+}$ has $25 - 2 = 23$ electrons, so $3d^5$.

Step 2. Unpaired electrons. The $d^2$ and $d^3$ ions have 2 and 3 unpaired electrons. Water is weak, so the $d^5$ ion keeps all 5 unpaired.

Step 3. Moments. $\sqrt{2 \times 4} = 2.83\ \text{BM}$. $\sqrt{3 \times 5} = 3.87\ \text{BM}$. $\sqrt{5 \times 7} = 5.92\ \text{BM}$.