The area enclosed by $2\left|x\right|+3\left|y\right|\le 6$ is

The given inequality is equivalent to the following system of inequalities.

$2x+3y\le 6$, when $x\ge 0,y\ge 0$

$2x-3y\le 6$, when $x\ge 0,y\le 0$

$-2x+3y\le 6,$ when $x\le 0,y\ge 0$

$-2x-3y\le 6$, when $x\le 0,y\le 0$

which represents a rhombus with sides

$2x+3y=6$ and $2x+3y=-6$

Length of the diagonals is 6 and 4 units along x-axis and
y-axis.

$\therefore$ The required area $=\frac{1}{2}\times 6\times 4=12$ sq. units.