1. Identify geometry and criterion for optical isomerism

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

We examine each complex one by one.

2. $\text{cis-}[\mathrm{Cr}(\mathrm{ox})_2\mathrm{Cl}_2]^{3-}$

• Oxalate $(\mathrm{ox})^{2-}$ is a bidentate ligand.
• Coordination number is $6$, so geometry is octahedral.
• Type: $[M(AA)_2a_2]$ with cis arrangement.

For octahedral complexes of type $\text{cis-}[M(AA)_2a_2]$, the cis form is optically active.

So, this complex shows optical isomerism.

3. $[\mathrm{Co}(\mathrm{en})_3]^{3+}$

• $\mathrm{en}$ (ethylenediamine) is a bidentate ligand.
• Geometry is octahedral.
• Type: $[M(AA)_3]$.

Such complexes have well-known $\Delta$ and $\Lambda$ forms, so they are optically active.

So, this complex shows optical isomerism.

4. $\text{cis-}[\mathrm{Pt}(\mathrm{en})_2\mathrm{Cl}_2]^{2+}$

• Here Pt is typically square planar in such complexes.
• In square planar geometry, the molecule lies in one plane, and that plane itself acts as a plane of symmetry.
• Therefore square planar complexes do not show optical isomerism.

So, this complex does not show optical isomerism.

5. $\text{cis-}[\mathrm{Co}(\mathrm{en})_2\mathrm{Cl}_2]^+$

• $\mathrm{en}$ is bidentate; coordination number $6$ gives octahedral geometry.
• Type: $\text{cis-}[M(AA)_2a_2]$.

As noted earlier, octahedral cis-$[M(AA)_2a_2]$ complexes are optically active.

So, this complex shows optical isomerism.

6. $\text{trans-}[\mathrm{Pt}(\mathrm{en})_2\mathrm{Cl}_2]^{2+}$

• Again Pt complex is square planar.
• Square planar complexes are planar and hence have a plane of symmetry.

So, this complex does not show optical isomerism.

7. $\text{trans-}[\mathrm{Cr}(\mathrm{ox})_2\mathrm{Cl}_2]^{3-}$

• Octahedral complex of type $\text{trans-}[M(AA)_2a_2]$.
• The trans form has symmetry elements (in particular, it is achiral).

So, this complex does not show optical isomerism.

8. Count the optically active complexes

Optically active ones are:

• $\text{cis-}[\mathrm{Cr}(\mathrm{ox})_2\mathrm{Cl}_2]^{3-}$
• $[\mathrm{Co}(\mathrm{en})_3]^{3+}$
• $\text{cis-}[\mathrm{Co}(\mathrm{en})_2\mathrm{Cl}_2]^+$

Thus, total number is

$3$

9. Comparison with stored answer

Stored correct answer = $4$

My derived answer = $3$

The likely source of mismatch is treating $\text{cis-}[\mathrm{Pt}(\mathrm{en})_2\mathrm{Cl}_2]^{2+}$ as optically active. But Pt(II) complexes are square planar, and square planar complexes are achiral due to planarity.