In the following reaction, the total number of oxygen atoms in X...

Let's first balance the two given chemical equations:

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

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

${Cl}_{2}{O}_{7} + {H}_{2}O ⟶ 2{HClO}_{4}\left(Y\right)$

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

So $X$ has one $O$ and $Y$ has four $O$.