[Co ( NH _ 3 ) _ 6 ] ^ 3 + and [ CoF _ 6 ] ^ 3 - are respectively...

In the complex ${\left[Co{\left({NH}_{3}\right)}_{6}\right]}^{3 +}$ Ammonia is strong field ligand and electronic configuration of 

${Co}^{3 +}$$⇒ 3{d}^{6}\left({t}_{2g}^{6}, {e}_{g}^{0}\right)$

Hybridisation: ${d}^{2}{sp}^{3}$

Pairing of electrons takes place due to the strong field ligand. Hence, it is inner orbital complex (spin paired complex).

In the complex ${\left[{CoF}_{6}\right]}^{3 -}$ fluoride is weak field ligand and electronic configuration of ${Co}^{3 +}$ $⇒ 3{d}^{6}\left({t}_{2g}^{4}, {e}_{g}^{2}\right)$.

Hybridisation: ${sp}^{3}{d}^{2}$

Pairing of electrons not takes place due to the weak field ligand. Hence, it is outer orbital complex (spin free complex).

Hence option B is the answer.