The difference in the coordination number of the central atom in the anionic and cationic part of ${\mathrm{Cl}}_2{\mathrm{O}}_6$ is 2.

${\mathrm{Cl}}_2{\mathrm{O}}_6\to {\mathrm{ClO}}_2^{+}+{\mathrm{ClO}}_4^{-}$

Co-ordination number = No. of atoms directly attached to an atom.

${\mathrm{ClO}}_2^{+}{\mathrm{ClO}}_4^{-}$

$$\begin{gathered} \mathrm{C}.\mathrm{N}=4-2 \\ \mathrm{C}.\mathrm{N}=2 \end{gathered}$$

Hence, the option C is correct.