Answer : Two electrons balances the charges in this half reaction.
Explanation :
The given half reaction is,
[tex]SO_2+2H_2O\rightarrow SO^{2-}_4+4H^+[/tex]
In this half reaction, there is no charges present on the left side of the reaction but on right side of the reaction, (2+) charge is present. So, two electrons (2-) are added on the right side of the reaction for balances the charge of the half reaction.
The balanced half reaction is,
[tex]SO_2+2H_2O\rightarrow SO^{2-}_4+4H^++2e^-[/tex]
Hence, two electrons balances the charges in this half reaction.