Step 1: Recall the trans-effect. In square-planar Pt(II) complexes, ligands differ in their ability to accelerate substitution of the ligand positioned trans to them (kinetic trans-effect). Strong \(\pi\)-acceptors and soft donors show a large trans-effect; hard, weak \(\sigma\)-donors show a small one.
Step 2: Rank the given ligands qualitatively.
\[
\text{(weak)} \text{H}_2\text{O} < \text{NH}_3 < \text{DMSO (via S)} < \text{C}_2\text{H}_4 \text{(strong)}
\]
\(\mathbf{H_2O}\): very weak \(\sigma\)-donor (hard base) \(⇒\) least trans-effect.
\(\mathbf{NH_3}\): slightly stronger \(\sigma\)-donor than water \(⇒\) larger effect than H\(_2\)O.
\(\mathbf{DMSO}\) (S-bound): softer donor, moderate trans-effect.
\(\mathbf{C_2H_4}\): \(\pi\)-acceptor olefin, strong trans-effect.
Step 3: Conclusion. Since H\(_2\)O has the smallest trans-effect in this set, the conversion will be slowest when \(L = \text{H}_2\text{O}\). Hence, option (A) is correct.