The total possible coordination isomers for the following compounds respectively are:
$\left[ {Co{{(en)}_3}} \right]\left[ {Cr{{({C_2}{O_4})}_3}} \right]$
$\left[ {Cu{{(N{H_3})}_4}} \right]\left[ {CuC{l_4}} \right]$
$\left[ {Ni{{(en)}_3}} \right]\left[ {Co{{(N{O_2})}_6}} \right]$
A. \[4,4,4\]
B. \[2,2,2\]
C. \[2,2,4\]
D. \[4,2,3\]

Hint: Coordination isomerism is a form of structural isomerism in which the composition of the coordination complex ion varies. In a coordination isomer the total ratio of ligand to metal remains the same, but the ligands attached to a specific metal ion change. Examples of a complete series of coordination isomers require at least two metal ions and sometimes more.

Complete step by step answer:
(i) The complex $\left[ {Co{{(en)}_3}} \right]\left[ {Cr{{({C_2}{O_4})}_3}} \right]$ has four possible isomers based on their spatial arrangements.
They are: $[Co{(en)_3}][Cr{({C_2}{O_4})_3}],[Co({C_2}{O_4}){(en)_2}][Cr{({C_2}{O_4})_2}(en)],[Co{({C_2}{O_4})_2}(en)][Cr({C_2}{O_4}){(en)_2}]$ and $[Co{({C_2}{O_4})_3}][Cr{(en)_3}]$
As we can clearly observe that there is a cross exchange of the ligands in the coordination complexes and thus, due to this, there exists a change in the spatial arrangement of the ligands around the central metal atom.
(ii) The complex $\left[ {Cu{{(N{H_3})}_4}} \right]\left[ {CuC{l_4}} \right]$ has four possible isomers based on their spatial arrangements.
They are:
$[Cu{(N{H_3})_4}][CuC{l_4}],[Cu{(N{H_3})_3}Cl][CuC{l_3}(N{H_3})],[Cu{(N{H_3})_2}C{l_2}][CuC{l_2}{(N{H_3})_2}]$ and $[Cu(N{H_3})C{l_3}][CuCl{(N{H_3})_3}]$
In this coordination complex also, we can clearly see that there is a cross exchange of the ammonia and chlorine ligands in the coordination complexes and thus, due to this, there exists a change in the spatial arrangement of the ligands around the central metal atom.
(iii) The complex $\left[ {Ni{{(en)}_3}} \right]\left[ {Co{{(N{O_2})}_6}} \right]$ has four possible isomers based on their spatial arrangements.
They are:
$[Ni{(en)_3}][Co{(N{O_2})_6}],[Ni{(en)_2}{(N{O_2})_2}][Co{(N{O_2})_4}(en)],[Ni(en){(N{O_2})_4}][Co{(N{O_2})_2}{(en)_2}]$ and $[Ni{(N{O_2})_6}][Co{(en)_3}]$
In this coordination complex too, there is a cross exchange of the ligands in the coordination complexes and thus, due to this, there exists a change in the spatial arrangement of the ligands around the central metal atom.
Thus the correct option is A. \[4,4,4\] .

Note:
In chemistry, isomers are molecules or polyatomic ions with identical molecular formulas, that is, the same number of atoms of each element but distinct arrangements of atoms in space. Isomerism is the existence or possibility of isomer formation. Isomers do not necessarily share similar chemical or physical properties.