Step 1: Understanding Fac-Mer Isomerism

Facial (fac) and meridional (mer) isomerism is a type of geometric isomerism observed in octahedral complexes with the general formula MA₃B₃. In the fac isomer, three identical ligands occupy the corners of one triangular face of the octahedron. In the mer isomer, the three identical ligands lie on a meridian (a plane passing through the metal atom).

Step 2: Analyzing the Options

We need to identify which complex fits the MA₃B₃ pattern:

• (A) $[Ni(en)_{2}(H_{2}O)_{2}]^{2+}$: This is an MA₂B₂ type (where en is bidentate). It shows cis-trans isomerism, not fac-mer.
• (B) $[Cr(py)_{3}(Cl)_{3}]$: This is an MA₃B₃ type where M=Cr, A=py, and B=Cl. This complex can exist in both fac and mer forms.
• (C) $[Cr(H_{2}O)_{6}]^{3+}$: This is an MA₆ type. It is highly symmetrical and does not show geometric isomerism.
• (D) $[Co(NH_{3})_{4}(H_{2}O)_{2}]^{3+}$: This is an MA₄B₂ type. It shows cis-trans isomerism, not fac-mer.

Step 3: Conclusion

Only the complex $[Cr(py)_{3}(Cl)_{3}]$ satisfies the structural requirement for facial and meridional isomerism.