Stability of complexes depends on factors like:
- Nature of ligand (strong or weak field)
- Chelate effect
- Charge on central metal ion
- Nature of metal
Analysis:
- (A) \([ \text{Ni(NH}_3)_6 ]\text{Cl}_2\): Involves monodentate ligand (NH\(_3\)) with moderate field strength. Stability is moderate.
- (B) \([ \text{Ag(NH}_3)_2 ]\text{Cl}\): Contains only two ammonia ligands; silver(I) forms labile complexes. Low stability.
- (C) \([ \text{Fe(en)}_2\text{Cl}_2 ]^+\): Contains bidentate ethylenediamine ligands (en) which provide some chelation. However, presence of Cl\(^{-}\) weakens stability.
- (D) \( \text{K}_4[ \text{Fe(CN)}_6 ] \): Cyanide (CN\(^{-}\)) is a strong field ligand forming very stable low-spin complexes with Fe(II). This makes it highly stable.
Therefore, the most stable complex is:
\[
\boxed{K_4[Fe(CN)_6]}
\]