Let's first balance the two given chemical equations:

${\mathrm{Na}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{O}⟶2\mathrm{NaOH}\left(\mathrm{X}\right)$

In this equation, there are two $\mathrm{NaOH}$ molecules, so the total number of oxygen atoms in the products is $1$.

${\mathrm{Cl}}_2{\mathrm{O}}_7+{\mathrm{H}}_2\mathrm{O}⟶2{\mathrm{HClO}}_4\left(\mathrm{Y}\right)$

In this equation, there are two ${\mathrm{HClO}}_4$ molecules, so the total number of oxygen atoms in the products is $4.$

So $\mathrm{X}$ has one $\mathrm{O}$ and $\mathrm{Y}$ has four $\mathrm{O}$.