Step 1: Recall when fac and mer isomers appear.
Facial (fac) and meridional (mer) isomerism shows up only in octahedral complexes of the type \([MA_3B_3]\): three of one monodentate ligand and three of another.
Step 2: Define the two isomers.
In the fac isomer the three identical ligands sit on one triangular face; in the mer isomer they lie along a meridian (an arc through the metal).
Step 3: Test option 2, \([Cr(py)_3Cl_3]\).
This has three pyridine and three chloride ligands, all monodentate. It is exactly the \(MA_3B_3\) type, so it shows fac and mer isomers.
Step 4: Test the other options quickly.
\([Ni(en)_2(H_2O)_2]^{2+}\) uses chelating en, not the \(A_3B_3\) pattern; \([Cr(H_2O)_6]^{3+}\) has six identical ligands; \([Co(NH_3)_4(H_2O)_2]^{3+}\) is an \(A_4B_2\) type giving cis and trans, not fac and mer.
Step 5: Eliminate and keep one.
Only \([Cr(py)_3Cl_3]\) fits the \(MA_3B_3\) requirement.
Step 6: State the answer.
The complex with fac and mer isomers is \([Cr(py)_3Cl_3]\), option 2.
\[ \boxed{[Cr(py)_3Cl_3]} \]