Identify the ligand and its charge

In the complex $[\text{Mn}(NCS)_6]^{x-}$, each thiocyanato ligand $NCS^-$ carries charge $-1$.

So, total ligand charge from 6 ligands is: $6 \times (-1) = -6$

Use the magnetic moment to find the number of unpaired electrons

The observed magnetic moment is given as: $\mu = 6.06\,\text{BM}$

Using the spin-only formula: $\mu = \sqrt{n(n+2)}$ where $n$ is the number of unpaired electrons.

Check for $n=5$: $\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92\,\text{BM}$

The observed value $6.06\,\text{BM}$ is very close to this, so the complex has 5 unpaired electrons.

Find oxidation state of Mn

Thiocyanate $NCS^-$ is a weak-field ligand, so the octahedral complex is high spin.

For Mn to have 5 unpaired electrons in an octahedral weak-field complex, it must be: $\text{Mn}^{2+} : 3d^5$

Calculate the charge on the complex

Let oxidation state of Mn be $+2$.

Then net charge on the complex is: $+2 + 6(-1) = +2 - 6 = -4$

Hence, $[\text{Mn}(NCS)_6]^{4-}$

Therefore, $x = 4$

Comparison with stored answer

Derived answer: $4$

Stored correct answer: $4$

They agree.