Step 1: Understanding the 18-electron rule.
The 18-electron rule states that transition metal complexes are most stable when they have 18 valence electrons, which are contributed by the metal and its ligands.
Step 2: Analyzing the complexes.
- \([Co(CO)_6]\) has 18 valence electrons (6 from CO and 12 from the metal). This obeys the 18-electron rule.
- \([Fe(CO)_4]^{2-}\) has 18 valence electrons (4 from CO and 14 from Fe). This obeys the 18-electron rule.
- \([HMn(CO)_5]\) has 18 valence electrons (5 from CO and 13 from Mn). This obeys the 18-electron rule.
- \([(η⁷-C₅H₅)RuCl(CO)(PPh₂)]\) has 17 valence electrons (1 from the \(\eta^7\)-C₅H₅, 1 from CO, and 1 from PPh₂). This complex does not obey the 18-electron rule.
Step 3: Conclusion.
The complex \([(η⁷-C₅H₅)RuCl(CO)(PPh₂)]\) does not obey the 18-electron rule, so the correct answer is (D).