The cobalt atom in $Hg \left[ Co ( SCN )_{4}\right]$ carries +2 charge and has $3 d ^{7}$ as the outer electronic configuration.

Here Hg shows +2 oxidation state and the compound is known as Mercuric tetrathiocyanatocobaltate(II).

It contains three unpaired electrons.

For three unpaired electrons, the expression becomes $\mu_{e f f}=\sqrt{3(3+2)} B \cdot M .=\sqrt{15} B \cdot M$

Therefore, option $C$ is correct.