Final answer:
There appears to be an error in the chemical formula provided in the question. Assuming H₂SO₂ was intended to be sulfurous acid (H₂SO₃), option (a) would reflect an equation close to being balanced for that compound.
Step-by-step explanation:
The correct balanced equation for the reaction between dihydrogen sulfite (H₂SO₂) and hydrogen iodide (HI) to produce hydrogen sulfide (H₂S), iodine (I₂), and water (H₂O) is not provided directly in the options given. However, understanding the principles of chemical reaction balancing and stoichiometry, we can do this by balancing each element on both sides of the reaction. The balanced reaction equation should have the same number of atoms of each element on both sides. The provided options within the context of the question seem to have an error as H₂SO₂ is not a common chemical compound and might be a typo or mistake. Potentially it should be H₂SO₃ (sulfurous acid) or H₂SO₄ (sulfuric acid), in which case option (a) would be close to correct balance if the compound was H₂SO₃. Still, it's important to confirm the correct reactants before finalizing the balancing.