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

Area of the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1\text{ is }\pi ab=\pi \left(2\right)\left(3\right)=6\pi$

Area of the rhombus formed of $\frac{\left|x\right|}{2}+\frac{\left|y\right|}{3}=1\text{ is }\frac{1}{2}\left(4\right)\left(6\right)=12$

Area enclosed by the region given of $\frac{\left|x\right|}{2}+\frac{\left|y\right|}{3}\ge 1\text{ and }\frac{x^2}{4}+\frac{y^2}{9}\le 1\text{ is }$

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