1. Identify the metal ion, oxidation state, geometry, and ligand strength in each complex

We compare crystal field splitting energy $\Delta$, which depends mainly on:

• oxidation state of the metal,
• geometry ($\Delta_o > \Delta_t$ generally, with $\Delta_t \approx \frac{4}{9}\Delta_o$),
• ligand field strength from the spectrochemical series.

Relevant ligand strengths: $\mathrm{CN^- > NH_3 > H_2O > Cl^-}$

Also, higher oxidation state gives larger $\Delta$.

2. Analyze each option

Option A: $[Co(NH_3)_5(H_2O)]Cl_3$

• Complex ion: $[Co(NH_3)_5(H_2O)]^{3+}$
• Since $NH_3$ and $H_2O$ are neutral ligands, oxidation state of Co is: $x = +3$
• So metal is $\mathrm{Co^{3+}}$
• Coordination number $=6$, so geometry is octahedral
• Ligands are mostly $NH_3$ with one $H_2O$, both moderate-field ligands

Thus, this has a fairly large $\Delta_o$.

Option B: $K_2[CoCl_4]$

• Complex ion: $[CoCl_4]^{2-}$
• Let oxidation state of Co be $x$: $x + 4(-1) = -2 \Rightarrow x=+2$
• So metal is $\mathrm{Co^{2+}}$
• Coordination number $=4$ with $Cl^-$, typically tetrahedral
• $Cl^-$ is a weak-field ligand
• Tetrahedral splitting is much smaller: $\Delta_t < \Delta_o$

Thus, this has relatively small splitting.

Option C: $[Co(NH_3)_5Cl]Cl_2$

• Complex ion: $[Co(NH_3)_5Cl]^{2+}$
• Let oxidation state of Co be $x$: $x + 5(0) + (-1) = +2 \Rightarrow x=+3$
• So metal is $\mathrm{Co^{3+}}$
• Coordination number $=6$, so octahedral
• Ligands: five $NH_3$ and one $Cl^-$
• Since $Cl^-$ is weaker than $H_2O$, this complex has smaller splitting than option A

So, $\Delta(C) < \Delta(A)$

Option D: $K_3[Co(CN)_6]$

• Complex ion: $[Co(CN)_6]^{3-}$
• Let oxidation state of Co be $x$: $x + 6(-1) = -3 \Rightarrow x=+3$
• So metal is $\mathrm{Co^{3+}}$
• Coordination number $=6$, hence octahedral
• Ligand $CN^-$ is a very strong-field ligand, much stronger than $NH_3$, $H_2O$, and $Cl^-$

Therefore this complex has very large octahedral splitting.

3. Compare all complexes

• B: $\mathrm{Co^{2+}}$, tetrahedral, weak ligand $Cl^-$ $\Rightarrow$ smallest
• C: $\mathrm{Co^{3+}}$, octahedral, but includes weak ligand $Cl^-$
• A: $\mathrm{Co^{3+}}$, octahedral, ligands stronger than in C
• D: $\mathrm{Co^{3+}}$, octahedral, strongest ligand $CN^-$

Hence, $\Delta_D > \Delta_A > \Delta_C > \Delta_B$

4. Final answer

The complex with the highest crystal field splitting energy is: $\boxed{K_3[Co(CN)_6]}$

So the correct option is D.