Let total mass of solution =100g
$\therefore$ mass of ethylene glycol $W_2=20g$
Mass of solvent (water) $W_1=80g$
Molar mass of $[C_2H_6O_2] M_1=12\times 2+6\times 16\times 2$
$\Rightarrow 24+6+32$
$\Rightarrow 62g mol^{-1}$
Molar mass of water $(H_2O) M_2=1\times 2+16$
$\Rightarrow 18g mol^{-1}$
Molar of water $n_1=\large\frac{W_1}{M_1}=\frac{80}{18}$$=4.44$ mole
Moles of $C_2H_6O_2$,
$n_2=\large\frac{W_2}{M_2}=\frac{20}{62}$
$\Rightarrow 0.322$ mol
Mole fraction of $C_2H_6O_2=\large\frac{n_2}{n_1+n_2}$
$\Rightarrow \large\frac{0.322}{4.44+0.322}$
$\Rightarrow 0.068$