A #3.6*g# mass of water was decomposed to give #3.2*g# dioxygen gas. What mass of dihydrogen gas was evolved?
We can immediately state that 0.4 g hydrogen gas will be produced.
Mass is conserved in every chemical reaction. So, if I start with 10 g of reactant I must finish with 10 g of product. You started with 3.6 g of water, and this mass was decomposed. You got 3.2 g oxygen gas, and the balance must have been the other constituent, hydrogen gas.
What the question tries to develop is an appreciation of the conservation of mass. 10 g, 10 kg, 10 tonnes, of reactant, NECESSARILY leads to 10 g, 10 kg, 10 tonnes of product.
As to the equation, this is simply gravy:
Is conservation of mass apparent here? Why and how?
Just on the question of balancing the equation, you could of course remove the half coefficient on dioxygen gas by doubling the entire equation. I have never seen the need to do so, inasmuch as the stoichiometry, the proportion of reactants and products, is easier to appreciate with the half coefficient.