The area (in sq.units) of the region out side $\frac{\left|x\right|}{2}+\frac{\left|y\right|}{3}=1$  and inside the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is 

$\frac{x^2}{4}+\frac{y^2}{9}=1\to \left(1\right)$

$\&\frac{1x1}{2}+\frac{1y1}{3}=1\to \left(2\right)$

Req.Area = Area of the 

ellipse -4(Area of $\Delta OAB$ )

$=\pi ab-4\left(\frac{1}{2}\times x-Int\times y-Int.)\right)$

$6\pi -12=6\left(\pi -2\right)$