Isn't that a line?

The area enclosed by $2|x| + 3|y| = 6$ is a rhombus having x-intercepts at $(\pm 3, 0)$ and y-intercepts at $(0, \pm 2)$ (see diagram below).

Therefore, the area is:

$A = 4 \times \left(\dfrac{3\times 2}{2}\right) = \boxed{12}$