Which of the following complex species does not involve ${\mathrm{d}}^2{\mathrm{sp}}^3$ hybridization?
 

 ${\mathrm{d}}^2{\mathrm{sp}}^3$ hybridization happens in an inner d-orbital complex. In an inner d-orbital complex strong field ligand is present. 

${\left[{\mathrm{CoF}}_6\right]}^{3-}$ is a weak field ligand, preventing inner orbital hybridization.
as the powerful field ligands, ${\mathrm{CN}}^{-}$, ${\mathrm{NH}}_3$ will exhibit inner orbital hybridization. 

Hence the correct answer is ${\left[{\mathrm{CoF}}_6\right]}^{3-}$