The hypothetical complex chlorodiaquatriamminecobalt(III) chloride can be represented as :
A. $[CoCl{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{2}}]C{{l}_{2}}$
B. $[Co{{(N{{H}_{3}})}_{3}}({{H}_{2}}O)C{{l}_{3}}]$
C. $[Co{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{2}}Cl]$
D. $[Co{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{3}}]C{{l}_{3}}$

Hint: The coordination compound is name by the IUPAC nomenclature system which is stated as the ligand name is written first and the metal atom name is written after that and at last the counter ion which is outside the coordination complex by applying the normal name.

Complete Step by Step Answer:
In the IUPAC system of nomenclature for the coordination complexes there are some rules which are stated in short as:
1.If positive counter ion is present it is written as first and if negative then at the last
2.The ligands attached to the metal atom is named at first in ascending order of the alphabets name of the resepective ligands with there no. of moles indicating as di,tri,tetra etc. and if the denticity of ligands are more then bis, tris, tetras etc. are used.
3.After the naming of metal atom its oxidation state in that complex is represented as in roman numerals and in bracket .
Using these rules we generally name any complex compounds . If we have a complex compound given then we can obtain its desired structural formula by using these concepts only just by reversing . Firstly we consider an coordination entity in which as the name given suggest the metal atom is cobalt with the oxidation number as +3 which can be represented as $[C{{o}^{+3}}$…..
As given in the name chlorodiaquatriamminecobalt(III) chloride chloro is used which means chlorine is present in 1 mol amount in the coordination entity as ligand , similarly it can be interpreted than diaqua means 2 moles of water which is ${{(N{{H}_{3}})}_{3}}$ ${{({{H}_{2}}O)}_{2}}$ is present as ligand in the coordination entity and also triammine which is 3 moles of ammonia ${{(N{{H}_{3}})}_{3}}$ should be there as ligand in the coordination entity. According to these informations we can determine the chemical formula of the complex which is inside the coordination entity that means $[CoCl{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{2}}]$ . Now chloride counter ion is also given which means Cl ion is present outside the coordination complex. To determine the no. of moles of chlorine required to be present outside the complex is determined by the net charge on the coordination entity which is to be balanced by the moles of chloride ion . which is +2 (+3-1+0+0) which can be balanced by the charge of -2 i.e 2 moles of chlorine is required.
Thus , the net complex formed can be represented as –
$[CoCl{{(N{{H}_{3}})}_{3}}{{({{H}_{2}}O)}_{2}}]C{{l}_{2}}$
And so the correct answer will be option A.

Note: The number of moles in the counter ion need to be balanced by the charge of the coordination entity not any number of counter ions can be written it should be taken care of.