Paramagnetic behaviour is directly proportional to the number of unpaired electrons ($n$). The magnetic moment is given by $\mu = \sqrt{n(n+2)}$ BM. Water ($H_2O$) is a weak field ligand , so these complexes are 'high spin', meaning electrons will occupy higher energy orbitals before pairing up (following Hund's rule).

1. $[Cr(H_2O)_6]^{2+}$ ($3d^4$): Configuration $t_{2g}^3 e_g^1$. Unpaired electrons ($n$) = 4.
2. $[Mn(H_2O)_6]^{2+}$ ($3d^5$): Configuration $t_{2g}^3 e_g^2$. Unpaired electrons ($n$) = 5 (Maximum) .
3. $[Fe(H_2O)_6]^{2+}$ ($3d^6$): Configuration $t_{2g}^4 e_g^2$. Pairing occurs in one $t_{2g}$ orbital. Unpaired electrons ($n$) = 4 .
4. $[Ni(H_2O)_6]^{2+}$ ($3d^8$): Configuration $t_{2g}^6 e_g^2$. The $t_{2g}$ set is fully filled (6 electrons), leaving 2 unpaired electrons in the $e_g$ set. Unpaired electrons ($n$) = 2 .

Since $Ni^{2+}$ has the minimum number of unpaired electrons (2), it exhibits the minimum paramagnetic behaviour.