${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$ and ${\left[{\mathrm{CoF}}_6\right]}^{3-}$ Are respectively known as:

${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$
${\mathrm{Co}}^{3+}\left(\text{strong field ligand}\right)\Rightarrow 3{\mathrm{d}}^6({\mathrm{t}}_{2\mathrm{g}}^6,{\mathrm{e}}_{\mathrm{g}}^0)\text{,}$
Hybridisation : ${\mathrm{d}}^2{\mathrm{sp}}^3$
Inner orbital complex(spin paired complex) pairing will take place.
${\left[{\mathrm{CoF}}_6\right]}^{3-}$
${\mathrm{Co}}^{3+}\left(\text{weak field ligand}\right)\Rightarrow 3{\mathrm{d}}^6({\mathrm{t}}_{2\mathrm{g}}^4,{\mathrm{e}}_{\mathrm{g}}^2)$
Hybridisation : ${\mathrm{sp}}^3{\mathrm{d}}^2$
Outer orbital complex (spin free complex), no pairing will take place