Which from following complexes does NOT obey EAN rule?

Effective Atomic Number analysis determines which complex violates the noble gas electron count rule.

The EAN equals the sum of metal valence electrons and ligand-donated electrons, aiming for Kr (36), Xe (54), or Rn (86). For monodentate ligands: $\text{EAN} = Z_{\text{metal}} - \text{oxidation state} + 2 \times \text{number of ligands}$.

For $\mathrm{Co}(\mathrm{NH}_3)_6^{3+}$: Co atomic number 27, oxidation state +3 gives 24 valence electrons; 6 $\mathrm{NH}_3$ donate 12 electrons. $\text{EAN} = 24 + 12 = 36$, satisfying the rule.

For $\mathrm{Cr}(\mathrm{CO})_6$: Cr atomic number 24, oxidation state 0 gives 24 valence electrons; 6 CO donate 12 electrons. $\text{EAN} = 24 + 12 = 36$, satisfying the rule.

For $\mathrm{Zn}(\mathrm{NH}_3)_4^{2+}$: Zn atomic number 30, oxidation state +2 gives 28 valence electrons; 4 $\mathrm{NH}_3$ donate 8 electrons. $\text{EAN} = 28 + 8 = 36$, satisfying the rule.

For $\mathrm{Cu}(\mathrm{NH}_3)_4^{2+}$: Cu atomic number 29, oxidation state +2 gives 27 valence electrons; 4 $\mathrm{NH}_3$ donate 8 electrons. $\text{EAN} = 27 + 8 = 35 \neq 36$, violating the rule.

The complex that does not obey the EAN rule is $\boxed{\text{D}}$.