1. Identify geometry and possible chirality

All the given complexes are octahedral, since each has coordination number $6$.

• $[Fe(NH_3)_2(CN)_4]^-$ is of type $[MA_2B_4]$
• $[CrCl_2(ox)_2]^{3-}$ is of type $[M(AA)_2B_2]$, where $AA$ is a bidentate ligand (oxalate)

A complex shows optical activity only if it is chiral, i.e. it has no plane of symmetry, no center of symmetry, and no improper axis.

2. Check options A and C: $[Fe(NH_3)_2(CN)_4]^-$

This is an octahedral complex of type $[MA_2B_4]$.

(A) cis-$[Fe(NH_3)_2(CN)_4]^-$

For octahedral $[MA_2B_4]$, the cis form has a plane of symmetry, so it is achiral. Hence it does not show optical activity.

(C) trans-$[Fe(NH_3)_2(CN)_4]^-$

The trans form has an inversion center and is therefore achiral. Hence it does not show optical activity.

So, A and C are not optically active.

3. Check options B and D: $[CrCl_2(ox)_2]^{3-}$

Here oxalate $(ox)$ is a symmetrical bidentate ligand. The complex is octahedral of type $[M(AA)_2B_2]$.

(B) trans-$[CrCl_2(ox)_2]^{3-}$

In the trans form, the two identical monodentate ligands ($Cl^-$) are opposite each other. This arrangement possesses symmetry elements (in particular, a plane/center of symmetry), so it is achiral. Thus, trans-$[CrCl_2(ox)_2]^{3-}$ does not show optical activity.

(D) cis-$[CrCl_2(ox)_2]^{3-}$

For octahedral complexes of type $[M(AA)_2B_2]$, the cis form can be chiral because the two bidentate ligands wrap around the metal in a helical manner, giving non-superimposable mirror images ($\Delta$ and $\Lambda$ forms). Therefore, cis-$[CrCl_2(ox)_2]^{3-}$ shows optical activity.

4. Conclusion

The complex that can show optical activity is:

$\boxed{\text{D: cis-}[CrCl_2(ox)_2]^{3-}}$

5. Comparison with stored correct answer

Stored correct answer: D

My derived answer: D

They agree.