X takes $2$ hours to mow the lawn
$\Rightarrow$ In $1$ hour he can mow $\frac{1}{2}$ of the lawn.
Y takes $4$ hours to mow the lawn
$\Rightarrow$ In $1$ hour he can mow $\frac{1}{4}$ of the lawn.
So in $1$ hr X and Y together can mow $\frac{1}{2}$+$\frac{1}{4}$ = $\frac{2+1}{4}$=$\frac{3}{4}$ of the lawn.
X and Y together can mow $\frac{3}{4}$ of the lawn in $1$ hour
$\Rightarrow$ X and Y together can mow $1$ lawn in $1* \frac{4}{3}$ hour = $60* \frac{4}{3}$ = $80$ minutes.
So Option B $80$ is the right answer.