Step 1: Reaction type.
Reduction of [Ni(CN)$_4$]$^{2-}$ with metallic potassium produces [Ni(CN)$_4$]$^{4-}$,
where Ni is in the +0 oxidation state.
Step 2: Electronic configuration.
Ni$^0$: 3d$^{10}$ configuration → fully filled d-orbitals, no unpaired electrons → diamagnetic.
Step 3: Geometry.
In the zero oxidation state, Ni forms tetrahedral complexes with CN$^-$ ligands.
Therefore, geometry = tetrahedral and magnetic nature = diamagnetic.
Step 4: Conclusion.
The correct answer is (B) Tetrahedral and diamagnetic.