Concept:
Optical isomerism arises when a molecule is chiral, meaning it is not superimposable on its mirror image. In coordination chemistry, optical isomerism is commonly observed in octahedral complexes containing bidentate ligands such as ethylenediamine (\(en\)).
Such complexes can exist as two non-superimposable mirror images known as enantiomers.
Step 1: Examine Option (A)
\[
[Co(NH_3)_4Cl_2]^+
\]
This complex exhibits geometrical isomerism (cis and trans forms).
However, both forms possess symmetry elements that make them achiral.
Therefore,
\[
\boxed{\text{No optical isomerism}}
\]
Step 2: Examine Option (B)
\[
[Co(en)_2Cl_2]^+
\]
The ligand \(en\) (ethylenediamine) is a bidentate ligand and forms chelate rings with the metal ion.
The cis form of this octahedral complex lacks a plane of symmetry and exists as two non-superimposable mirror images.
Therefore, the complex exhibits optical isomerism.
\[
\boxed{\text{Optically Active}}
\]
Step 3: Examine Option (C)
\[
[Co(NH_3)_5Cl]^{2+}
\]
This complex possesses considerable symmetry and does not form optical isomers.
Hence,
\[
\boxed{\text{Optically Inactive}}
\]
Step 4: Examine Option (D)
\[
[Co(NH_3)_6]^{3+}
\]
All six ligands are identical.
The complex possesses a high degree of symmetry and therefore cannot exhibit chirality.
Hence,
\[
\boxed{\text{Optically Inactive}}
\]
Step 5: Final Conclusion
Among the given compounds, only
\[
[Co(en)_2Cl_2]^+
\]
can exist as a pair of non-superimposable mirror images.
Therefore, it exhibits optical isomerism.
\[
\boxed{\text{Option (B)}}
\]