To determine which complex can show fac- and mer- isomerism, we need to understand what these isomers are:
Facial (fac-) and Meridional (mer-) Isomerism:
Fac- and mer- isomerism typically occurs in octahedral complexes with a formula of the type $Ma_3b_3$, where a and b are different ligands.
Let's analyze each option:
Therefore, the correct answer is $[Co(NH_3)_3(NO_2)_3]$ as it is the only complex that can exhibit both fac- and mer- isomerism.