We will determine the oxidation states of Mn in the reactants and products. For MnO$_4^{2-}$, let the oxidation state of Mn be $x$. Then $x + 4(-2) = -2$, yielding $x = +6$. For MnO$_4^-$, $x + 4(-2) = -1$, so $x = +7$. For MnO$_2$, $x + 2(-2) = 0$, resulting in $x = +4$. The Mn oxidation states in this reaction are +6, +7, and +4. Consequently, the oxidation states not explicitly shown are +2 and +3.