1. Find the oxidation state of the metal in each compound and compare it with the maximum oxidation state shown by that metal.

2. Option A: $MnO_2$ and $CrO_2Cl_2$

• In $MnO_2$: $x + 2(-2) = 0$ $x - 4 = 0 \,\Rightarrow\, x = +4$ So Mn is in $+4$ state.

  Highest oxidation state of Mn is $+7$, so this is not highest.

• In $CrO_2Cl_2$: Let oxidation state of Cr be $x$. $x + 2(-2) + 2(-1) = 0$ $x - 4 - 2 = 0 \Rightarrow x = +6$ Highest oxidation state of Cr is $+6$, so this is highest.

Thus in option A, only Cr is at highest oxidation state, not Mn. So A is not correct.

3. Option B: $[NiCl_4]^{2-}$ and $[CoCl_4]^{2-}$

• In $[NiCl_4]^{2-}$: $x + 4(-1) = -2$ $x - 4 = -2 \Rightarrow x = +2$ Highest oxidation state of Ni is about $+4$, so not highest.

• In $[CoCl_4]^{2-}$: $x + 4(-1) = -2$ $x - 4 = -2 \Rightarrow x = +2$ Highest oxidation state of Co is $+5$ (or commonly $+3$ in introductory treatment), so not highest.

So B is not correct.

4. Option C: $[Fe(CN)_6]^{3-}$ and $[Cu(CN)_4]^{2-}$

• In $[Fe(CN)_6]^{3-}$: Each $CN^-$ is $-1$. $x + 6(-1) = -3$ $x - 6 = -3 \Rightarrow x = +3$ Highest oxidation state of Fe is $+6$, so not highest.

• In $[Cu(CN)_4]^{2-}$: $x + 4(-1) = -2$ $x - 4 = -2 \Rightarrow x = +2$ Highest oxidation state of Cu is $+3$, so not highest.

So C is not correct.

5. Option D: $[FeCl_4]^-$ and $Co_2O_3$

• In $[FeCl_4]^-$: $x + 4(-1) = -1$ $x - 4 = -1 \Rightarrow x = +3$ Highest oxidation state of Fe is $+6$, so not highest.

• In $Co_2O_3$: $2x + 3(-2) = 0$ $2x - 6 = 0 \Rightarrow x = +3$ Highest oxidation state of Co is $+5$ (or at least not restricted to $+3$), so not highest.

So D is not correct.

6. Conclusion

By strict oxidation-state analysis, none of the given options contains both metals in their highest oxidation state.

However, in many exam keys, option A is marked because $Cr$ in $CrO_2Cl_2$ is definitely in its highest oxidation state $+6$, and the question may have intended a different manganese compound or used a flawed key. But $Mn$ in $MnO_2$ is only $+4$, whereas Mn attains up to $+7$.

Therefore, the stored answer A is chemically inconsistent.