Step 1: For [NiCl$_2$(PPh$_3$)$_2$].
Ni is in +2 oxidation state → 3d$^8$ configuration.
Cl$^-$ and PPh$_3$ are weak field ligands → complex is paramagnetic.
Unpaired electrons = 2.
Spin-only magnetic moment,
\[
\mu = \sqrt{n(n+2)} = \sqrt{2(2+2)} = \sqrt{8} = 2.83\ \text{BM.}
\]
Step 2: For [Mn(NCS)$_6$]$^{4-}$.
Mn is in +2 oxidation state → 3d$^5$ configuration.
All ligands are weak field (high-spin complex).
Unpaired electrons = 5.
\[
\mu = \sqrt{5(5+2)} = \sqrt{35} = 5.92\ \text{BM.}
\]
Step 3: Conclusion.
Hence, magnetic moments are 2.83 BM and 5.92 BM, respectively.