Hydrogen peroxide and water contain $5.$$93\%$ and $11.2\%$ of hydrogen respectively. The data illustrates the law of? 

For hydrogen peroxide, $100 \text{g}$ of sample contains $5.93$ $\mathrm{g}$ of hydrogen, thus the amount of oxygen in hydrogen peroxide will be $100-5.93=94.07\text{ g}$.

The ratio of mass of oxygen to the hydrogen in the given sample of hydrogen peroxide is given as:

$\frac{94.07}{5.93}=15.86$

Similarly, for water, $100 \text{g}$ of sample contains $11.2$ $\text{g}$ of hydrogen and the amount of oxygen in water will be $100-11.2=88.8 \text{g}$

The ratio of mass of oxygen to the hydrogen in the given sample of water is:

$\frac{88.8}{11.2}=7.93$

Thus, the two ratios are in the proportion $\frac{15.86}{7.93}=2:1$

Therefore, the given data illustrates the law of multiple proportions.

Hence option (B) is correct.