Step 1: Determine the equivalent weight of the oxidizing agent.
The oxidizing agent in this reaction is \( \text{SO}_2 \), and its equivalent weight is determined by the amount of oxygen it can provide in the reaction.
The reaction shows that 1 mole of \( \text{SO}_2 \) is reduced to 1 mole of sulfur (S), and 2 moles of \( \text{H}_2\text{O} \) are converted to 2 moles of \( \text{H}_2\text{O}_2 \), with oxygen being released.
The equivalent weight of \( \text{SO}_2 \) is the molar mass divided by the number of electrons transferred in the reaction. Since 2 electrons are involved, the equivalent weight of \( \text{SO}_2 \) is half of its molar mass.
Step 2: Find the choice that has twice the equivalent weight.
The molar mass of \( \text{SO}_2 \) is 64 g/mol, so the equivalent weight is:
\[
\frac{64}{2} = 32 \, \text{g}
\]
The choice with twice the equivalent weight is \( 64 \, \text{g of H}_2\text{O} \), which corresponds to option (4).
Step 3: Conclusion.
The correct answer is \( 64 \, \text{g of H}_2\text{O} \), which is option (4).