Step 1: Understand net charge of coordination compounds.
The net charge of a complex is calculated by summing the charges of the central metal ion and all the ligands present inside the coordination sphere.
Step 2: Analyze each option.
(A) $[Ni(NH_3)_6]Cl_2$: The complex ion is $[Ni(NH_3)_6]^{2+}$, so it carries a positive charge.
(B) $[Fe(H_2O)_6]Cl_3$: The complex ion is $[Fe(H_2O)_6]^{3+}$, hence it is charged.
(C) $K_2[HgI_4]$: The complex ion is $[HgI_4]^{2-}$, which is negatively charged.
(D) $[Pt(NH_3)_2Cl_2]$: Platinum is in +2 oxidation state, two $NH_3$ ligands are neutral, and two $Cl^-$ ligands contribute −2 charge, resulting in an overall neutral complex.
Step 3: Conclusion.
$[Pt(NH_3)_2Cl_2]$ carries no net charge.