The stability of complexes is often related to the value of \( \Delta \), which is the energy difference between the d-orbitals in the ligand field. Higher \( \Delta \) values typically correspond to more stable complexes.
Based on the \( \Delta \) values:
- \( [{Fe(CN)}_6]^{3-} \) has the highest \( \Delta \) value due to the strong field ligand \( {CN}^- \), making it the most stable complex.
- \( [{Co(CN)}_6]^{3-} \) is slightly less stable compared to \( [{Fe(CN)}_6]^{3-} \).
- \( [{Mn(CN)}_6]^{3-} \) has the lowest \( \Delta \) value and is the least stable among these complexes. Thus, the correct increasing order of stability is \( {III}<{II}<{IV}<{I} \).