Step 1: Understanding Ligand Field Strength.
The strength of the ligand field influences the d-orbital splitting in transition metal complexes. Strong field ligands cause a large splitting of the d-orbitals, while weak field ligands cause a smaller splitting. The ligand field strength follows the trend:
\[
\text{CN}^- > \text{CO}_4^{2-} > \text{NH}_3 > \text{OH}^-
\]
Step 2: Analyzing the Ligands.
- (A) NH\(_3\) is a weak field ligand.
- (B) C\(_2\)O\(_4^{2-}\) (oxalate) is a moderate field ligand.
- (C) OH\(^-\) is a weaker field ligand compared to NH\(_3\).
- (D) CN\(^-\) is a strong field ligand, causing the largest splitting.
Step 3: Conclusion.
Thus, the order of increasing d-orbital splitting is:
\[
\text{OH}^- < \text{C}_2\text{O}_4^{2-} < \text{NH}_3 < \text{CN}^-
\]
So, the correct answer is option (4): (C), (B), (A), (D).