1. Identify the metal ion and oxidation state in each complex

All four complexes contain iron in the $+3$ oxidation state:

• $[\mathrm{Fe(C_2O_4)_3}]^{3-}$
• $[\mathrm{Fe(CN)_6}]^{3-}$
• $[\mathrm{Fe(NH_3)_6}]^{3+}$
• $[\mathrm{FeF_6}]^{3-}$

So in all cases, the metal is $\mathrm{Fe^{3+}}$.

For $\mathrm{Fe}$:

Thus,

Since the metal ion is the same in all complexes, the splitting depends mainly on the nature of ligand.

2. Use spectrochemical series

Magnitude of octahedral crystal field splitting $\Delta_o$ depends on ligand strength.

Relevant part of the spectrochemical series is:

So ligand field strength increases in the order:

Hence, for the same metal ion $\mathrm{Fe^{3+}}$, the complex with $\mathrm{CN^-}$ will produce the largest splitting.

3. Evaluate each option

• A: $[\mathrm{Fe(C_2O_4)_3}]^{3-}$
  Oxalate is a moderate ligand.

• B: $[\mathrm{Fe(CN)_6}]^{3-}$
  $\mathrm{CN^-}$ is a very strong field ligand, so this gives the largest $\Delta_o$.

• C: $[\mathrm{Fe(NH_3)_6}]^{3+}$
  $\mathrm{NH_3}$ is stronger than oxalate and fluoride, but weaker than cyanide.

• D: $[\mathrm{FeF_6}]^{3-}$
  $\mathrm{F^-}$ is a weak field ligand, so this gives the smallest splitting among these.

4. Conclusion

The complex showing the largest splitting of $d$-orbitals is:

So, Option B is correct.