The area of region bounded by the line 2x + y = 8, the Y-axis and the lines y = 2 and y = 4 is 

$\mathrm{x}=4-\frac{1}{2}\mathrm{y}$

$\therefore$Required area = Area of region P Q R S P
= Area between the line $x=4-\frac{1}{2}y$
the Y-axis and the lines y=2 and y=4
$\begin{array}{l}={\int }_2^4 \mathrm{xdy}={\int }_2^4 \left(4-\frac{1}{2}\mathrm{y}\right)\mathrm{dy}\\ ={\left[4\mathrm{y}-\frac{{\mathrm{y}}^2}{4}\right]}_2^4=(16-4)-(8-1)\\ =12-7=5\text{ sq units }\end{array}$
The given line AB is 2x + y = 8