Step 1: The balancing idea.
The charge written on top of a complex is just the leftover charge after we add up the metal's own charge and the charge of every ligand. So if we know the ligand charges, we can work backwards to the metal.
Step 2: Charges of the groups present.
Inside $\mathrm{[Pt(en)_2Cl_2]^{2+}}$ we have two 'en' molecules and two chlorides. Ethylenediamine (en) is a neutral molecule, so each contributes nothing to the charge. Each chloride carries $-1$, and there are two, so together the chlorides bring $-2$.
Step 3: Build the charge equation.
Call platinum's oxidation number $x$. Everything must total the overall charge of $+2$:
\[ x + 2(0) + 2(-1) = +2 \]
Step 4: Solve it.
This gives $x - 2 = +2$, so $x = +4$. Platinum therefore sits in the $+4$ state.
\[ \boxed{\text{Option (B): Pt is } +4} \]