To solve this problem, we need to understand the factors affecting the color of complexes, specifically the energy absorbed due to d-d transitions.$\newline$The energy absorbed is related to the ligand field strength, which is influenced by the ligands present in the complex.$\newline$Given complexes:$\newline$(A) $[$Ni(H$_2O)_2($en$)_2]^{2+} \newline$(B) $[$Ni(H$_2O)_4($en$)]^{2+} \newline$(C) $[$Ni(en)$_3]^{2+} \newline$The ligands involved are:$\newline$• $$H$_2O$ (a weak field ligand)$\newline$• $$en (ethylenediamine, a strong field ligand)$\newline$The strength of the ligand field affects the splitting of the d-orbitals, which in turn affects the energy absorbed.$\newline$• More strong field ligands lead to greater splitting and higher energy absorption.$\newline$Analyzing the complexes:$\newline$• Complex (A) has 2 $$H$_2O$ and 2 en ligands.$\newline$• Complex (B) has 4 $$H$_2O$ and 1 en ligand.$\newline$• Complex (C) has 3 en ligands.$\newline$Order of ligand field strength:$$en$>$H$_2O \newline$Therefore, the order of energy absorbed is determined by the number of strong field ligands (en):$\newline$• Complex (C) has the highest number of en ligands, leading to the highest energy absorption.$\newline$• Complex (A) has more en ligands than complex (B), leading to higher energy absorption than (B).$\newline$Thus, the correct order of energy absorbed is:$\newline$C > A > B$\newline$This corresponds to Option 3.