Why `[Co(NH_3)_6]^(3+)` is an inner orbital complex where is `[Ni(NH_3)_6]^(2+)` is an outer orbital complex ?

Explanation

In these complexes central metal ions are `Co^(3+) and Ni^(2+)`

`NH_3` is a strong field ligand. It can cause pairing of unpaired electrons. In `[Co(NH_3)_6]^(3+)`, if electron spins of `Co^(3+)` undergoes `d^2sp^3` hybridisation by using two empty 3d orbitals. The complex is inner orbital complex.
In `[Ni(NH_3)_6]^(2+)`, if electron spins of `Ni^(2+)` are paired up only one empty 3d orbital will be created. Thus `Ni^(2+)` undergoes `sp^3d^2` hybridization by using two empty 4d-orbitals.The complex is an outer orbital complex.