When central metal ion is same (here $Ni ^{2+}$ ), the absorption of colour depends on the, ligand. According to spectrochemical series, various ligands are as follows
$I ^{-}< Br ^{-}< Cl ^{-}< NO _{3}^{-}< F ^{-}< H _{2} O < NH _{3} < NO _{2}^{-}< CN ^{-}< CO$
Thus, $H _{2} O$ is weakest ligand among these, therefore, the absorbed energy will be lowest in $\left[ Ni \left( H _{2} O \right)_{6}\right]^{2+}$, so it will absorb highest wavelength (red light) $\left(E \propto \frac{1}{\lambda}\right)$
$\therefore $ the order of increasing wavelength is
$\left[ Ni \left( NO _{2}\right)_{6}\right]^{4-}<\left[ Ni \left( NH _{3}\right)_{6}\right]^{2+}<\left[ Ni \left( H _{2} O \right)_{6}\right]^{2+}$