The reaction pathway that starts with sulfur dioxide (SO2) and ends with zinc hydroxide (Zn(OH)2) involves several steps.

SO2 is oxidized to SO3 in the presence of oxygen.
2SO2 + O2 -> 2SO3

SO3 reacts with water to form sulfuric acid (H2SO4).
SO3 + H2O -> H2SO4

Sulfuric acid donates a proton to form bisulfate ions (HSO4^-).
H2SO4 -> H^+ + HSO4^-

Zinc sulfate (ZnSO4) dissociates into zinc ions (Zn^2+) and sulfate ions (SO4^2-).
ZnSO4 -> Zn^2+ + SO4^2-

Zinc ions react with hydroxide ions (OH^-) to form zinc hydroxide (Zn(OH)2).
Zn^2+ + 2OH^- -> Zn(OH)2

Overall reaction:
2SO2 + O2 + 2H2O + ZnSO4 -> 2H2SO4 + Zn(OH)2

Note: This is a general overview of the reaction pathway. Depending on the conditions of the reaction, additional intermediate steps or side reactions may occur.