The atomic masses of elements are :-

$\mathrm{Na}= 23\mathrm{g}/\mathrm{mol}; \mathrm{S}=32\mathrm{g}/\mathrm{mol};\mathrm{O}=16\mathrm{g}/\mathrm{mol};\mathrm{H}=1\mathrm{g}/\mathrm{mol}$

So, the molecular mass of ${\mathrm{Na}}_2{\mathrm{SO}}_4·10{\mathrm{H}}_2\mathrm{O}$=$23\times 2+32+14\times 16+20\times 1=322\mathrm{g}/\mathrm{mol}$

Given mass of ${\mathrm{Na}}_2{\mathrm{SO}}_4·10{\mathrm{H}}_2\mathrm{O}=32.2 \mathrm{g}$

Mole of ${\mathrm{Na}}_2{\mathrm{SO}}_4·10{\mathrm{H}}_2\mathrm{O}=\frac{\mathrm{Given} \mathrm{mass}}{\mathrm{Molecular} \mathrm{mass}}=\frac{32.2}{322}=0.1 \mathrm{mol}$

Now, the atomicity of oxygen is $14$.

So, mole of oxygen = $\mathrm{Mole} \mathrm{of} {\mathrm{Na}}_2{\mathrm{SO}}_4·10{\mathrm{H}}_2\mathrm{O} \times \mathrm{atomicity} \mathrm{of} \mathrm{oxygen} =0.1\times 14=1.4 \mathrm{mol}$

So, mass of oxygen = $1.4\times 16=22.4 \mathrm{g}$

Hence, the number of grams of oxygen is $22.4 \mathrm{g}$.