We need a complex for which:

• $\Delta_o = 0$ effectively means CFSE = 0 in octahedral field, i.e. electron distribution gives zero crystal field stabilization.
• $\mu = 5.96$ B.M. means spin-only magnetic moment corresponding to $\mu = \sqrt{n(n+2)}$ where $n$ is number of unpaired electrons.

Find $n$ from $\mu = 5.96$ B.M. $\sqrt{n(n+2)} = 5.96 \approx \sqrt{35}$ Hence, $n(n+2)=35$ $n=5$ So the complex must have 5 unpaired electrons.

Now check which octahedral configuration has CFSE = 0 and 5 unpaired electrons.

For octahedral splitting, CFSE is zero for:

• high-spin $d^5$ : $t_{2g}^3 e_g^2$
• high-spin $d^0$, $d^{10}$ also, but those do not give 5 unpaired electrons.

Thus we need a high-spin $d^5$ complex.

Evaluate each option.

Option A: $[\mathrm{FeF}_6]^{4-}$

• Oxidation state of Fe: $x + 6(-1) = -4 \Rightarrow x=+2$
• So Fe is $\mathrm{Fe}^{2+}$, i.e. $d^6$.
• $F^-$ is weak field, so high-spin $d^6$.
• High-spin $d^6$ has 4 unpaired electrons, not 5.
• Also CFSE is not zero.
• Not correct.

Option B: $[\mathrm{Mn}(\u200b\mathrm{SCN})_6]^{4-}$

• Oxidation state of Mn: $x + 6(-1) = -4 \Rightarrow x=+2$
• So Mn is $\mathrm{Mn}^{2+}$, i.e. $d^5$.
• $SCN^-$ is a weak-field ligand here, so complex is high spin.
• High-spin $d^5$ in octahedral field: $t_{2g}^3 e_g^2$
• Number of unpaired electrons $=5$.
• Magnetic moment: $\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ B.M.}$ commonly written close to $5.96$ B.M.
• CFSE: $\text{CFSE} = 3(-0.4\Delta_o) + 2(+0.6\Delta_o)= -1.2\Delta_o +1.2\Delta_o=0$
• Correct.

Option C: $[\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}$

• Oxidation state of Co is $+3$, so $\mathrm{Co}^{3+}$ is $d^6$.
• With $NH_3$ and $\mathrm{Co}^{3+}$, this is low-spin $d^6$.
• Low-spin $d^6: t_{2g}^6 e_g^0$, so 0 unpaired electrons.
• Not correct.

Option D: $[\mathrm{Fe}(\mathrm{CN})_6]^{4-}$

• Oxidation state of Fe: $x + 6(-1) = -4 \Rightarrow x=+2$
• So $\mathrm{Fe}^{2+}$ is $d^6$.
• $CN^-$ is strong field, so low-spin $d^6$.
• Low-spin $d^6$ has 0 unpaired electrons.
• Not correct.

Therefore the only complex with zero CFSE and magnetic moment near $5.96$ B.M. is: $[\mathrm{Mn}(\mathrm{SCN})_6]^{4-}$