Identify the geometry of a complex compound [CoF_6]^ -3 .

The given complex is $[\text{CoF}_6]^{3-}$.

The central metal atom is Cobalt (Co). Let its oxidation state be $x$.

$x + 6(-1) = -3 \Rightarrow x = +3$

The electronic configuration of Co is $[\text{Ar}] 3d^7 4s^2$.

The electronic configuration of Co^{3+}$is$[$\text{Ar}$] 3d^6$.<br><br>Since F^-$ is a weak field ligand, it does not cause pairing of electrons in the $3d$ orbitals.

The complex undergoes $sp^3d^2$ hybridization to accommodate six F^- ligands.

For a coordination number of 6, the geometry of the complex is octahedral.

Answer: Octahedral