The Irving-Williams series outlines the trend in stability constants for complexes formed by divalent first-row transition metal ions (like Mn$^{2+}$ through Zn$^{2+}$).
The question asks for the metal ion (M) in the complex $[M(EDTA)]^{2-}$ that possesses the highest overall stability constant ($\log \beta$). Based on the Irving-Williams series, Copper (Cu$^{2+}$) typically forms the most stable complexes among these ions.
To find the number of d electrons for the relevant ion, we examine the electron configuration of Copper (atomic number 29).
The electron configuration of a neutral Copper atom is: $[Ar] 3d^{10} 4s^1$.
When forming the divalent ion, Cu$^{2+}$, two electrons are removed. The electron is lost first from the 4s orbital, and then from the 3d orbital.
The electron configuration for the Cu$^{2+}$ ion is: $[Ar] 3d^9$.
Therefore, the Cu$^{2+}$ ion contains 9 d electrons.
Consider the figure given below, where M is a metal and L is a monodentate ligand. The $\sigma$-bonding ligand group orbital (LGO) having same symmetry with $d_{z^2}$ orbital of M in the octahedral coordination geometry is
Among the given platinum(II) complexes, the one that is thermally the most unstable is