As the ligand field strength increases, the energy of light absorbed by the complex also increases. Since wavenumber $\bar{\nu} \propto$ energy of absorbed light, the order of wavenumber depends on the ligand strength.
For [Co(CN)$_6$]$^{3-}$ (B), CN$^-$ is a strong field ligand (highest $\bar{\nu}$).
For [Co(NH$_3$)$_5$(H$_2$O)]$^{3+}$ (C), NH$_3$ and H$_2$O have moderate ligand field strength.
For [Cu(H$_2$O)$_4$]$^{2+}$ (D), H$_2$O is a weaker field ligand.
For [CoCl(NH$_3$)$_5$]$^{2+}$ (A), Cl$^-$ is the weakest field ligand (lowest $\bar{\nu}$).
Thus, the order is:
\[D < A < C < B.\]
Let a line passing through the point $ (4,1,0) $ intersect the line $ L_1: \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} $ at the point $ A(\alpha, \beta, \gamma) $ and the line $ L_2: x - 6 = y = -z + 4 $ at the point $ B(a, b, c) $. Then $ \begin{vmatrix} 1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c \end{vmatrix} \text{ is equal to} $