Law of Multiple Proportions states that "When two elements form a series of compounds, the ratio of the masses of the 1st element that combine with 1 g of the other element can always be reduced to small whole numbers"

In order to confirm the Law of Multiple Proportions here, we need to  calculate the mass of H over mass of O to find how much g of H is in 1 g of O

Hydrogen peroxide is composed of a peroxide ion (O₂^2-) and 2 H⁺ atoms. Recall that compounds, the charge of the ion goes to the subscript of the counterion. Hydrogen peroxide will appear as H₂O₂

Calculating the proportions of H and O for water and hydrogen peroxide: