1. Find the oxidation state and d-configuration of Co in each complex

For all given complexes, cobalt is in the +3 oxidation state:

• $[Co(CN)_6]^{3-}$: $x + 6(-1) = -3 \Rightarrow x = +3$
• $[Co(C_2O_4)_3]^{3-}$: $x + 3(-2) = -3 \Rightarrow x = +3$
• $[Co(H_2O)_6]^{3+}$: $H_2O$ is neutral, so $x = +3$
• $[Co(NH_3)_6]^{3+}$: $NH_3$ is neutral, so $x = +3$

So in every case, the metal ion is $Co^{3+}$.

Cobalt has atomic number $27$:

$Co: [Ar]3d^74s^2$

Thus,

$Co^{3+} : [Ar]3d^6$

Since the metal ion is the same in all complexes, the magnitude of $\Delta_o$ depends mainly on the nature of the ligand.

2. Use spectrochemical series

The octahedral crystal field splitting increases with ligand field strength.

Relevant part of the spectrochemical series is:

$C_2O_4^{2-} < H_2O < NH_3 < CN^-$

Thus, among the given ligands:

• $CN^-$ is the strongest field ligand
• $NH_3$ is stronger than $H_2O$
• Oxalate $\left(C_2O_4^{2-}\right)$ is weaker than both $H_2O$ and $NH_3$

Therefore,

$\Delta_o([Co(CN)_6]^{3-}) > \Delta_o([Co(NH_3)_6]^{3+}) > \Delta_o([Co(H_2O)_6]^{3+}) > \Delta_o([Co(C_2O_4)_3]^{3-})$

3. Evaluate the options

• A: $[Co(CN)_6]^{3-}$ — strongest ligand $CN^-$, so largest $\Delta_o$
• B: $[Co(C_2O_4)_3]^{3-}$ — oxalate is weaker, so not highest
• C: $[Co(H_2O)_6]^{3+}$ — weaker than $NH_3$ and $CN^-$
• D: $[Co(NH_3)_6]^{3+}$ — strong, but still weaker than $CN^-$

Hence, the highest value of $\Delta_o$ is for:

$\boxed{[Co(CN)_6]^{3-}}$

So, option A is correct.