The observed magnetic moment of the complex [ Mn ( NCS ) 6 ) ] x - is 6 . 06   BM . The numerical value…

The complex $\left[\mathrm{Mn}\right(\mathrm{NCS}{)}_6){]}^{\mathrm{x}-}$ has a magnetic moment of$6.06 \mathrm{BM}$. This indicates that the complex has unpaired electrons, which contribute to its magnetic moment.

Number of unpaired electrons $=5$$({\mathrm{Mn}}^{2+} : 3{\mathrm{d}}^5)$.
So $\mathrm{Mn}$ must be in $+2$ oxidation state ${\mathrm{Mn}}^{2+}$.

$$\begin{gathered} \Rightarrow 2 + (–6) = –\mathrm{x} \\ \Rightarrow –4 = –\mathrm{x} \\ \Rightarrow \mathrm{x} = 4 \end{gathered}$$
The numerical value of $\mathrm{x}$ is $4$, so the complex is $\left[\mathrm{Mn}\right(\mathrm{NCS}{)}_6){]}^{4-}$.