The pair of compounds having metals in their highest oxidation state is

$$\begin{gathered} {\mathrm{MnO}}_2 \\ \mathrm{x}+2(-2)=0 \end{gathered}$$

  $x = +4$

$$\begin{gathered} {\mathrm{CrO}}_2\mathrm{Cl} \\ \mathrm{x}+2(-2)+\left(1\right(-1\left)\right)=0 \end{gathered}$$

$x = +6$

$$\begin{gathered} [{\mathrm{FeCl}}_4{]}^{-} \\ \mathrm{x}+4(-1)=-1 \end{gathered}$$

$x = +3$

$$\begin{gathered} {\mathrm{Co}}_2{\mathrm{O}}_3 \\ 2\mathrm{x}+3(-2)=0 \end{gathered}$$

$x = +3$

$$\begin{gathered} [\mathrm{Fe}(\mathrm{CN}{)}_6{]}^{3-} \\ \mathrm{x}+6(-1)=-3 \end{gathered}$$

$x = +3$

$$\begin{gathered} [\mathrm{Cu}(\mathrm{CN}{)}_4{]}^{2-} \\ \mathrm{x}+4(-1)=-2 \end{gathered}$$

$x = +2$

$$\begin{gathered} [{\mathrm{NiCl}}_4{]}^{2-} \\ \mathrm{x}+4(-1)=-2 \end{gathered}$$

$x = +2$

$$\begin{gathered} [{\mathrm{CoCl}}_4{]}^{2-} \\ \mathrm{x}+4(-1)=-2 \end{gathered}$$

$x = +2$

Hence the pair of compounds which have highest oxidation number are

${\mathrm{MnO}}_2$ and ${\mathrm{CrO}}_2{\mathrm{Cl}}_2$.