The area enclosed by the curve 2|x| + 3|y| = 6 is

We can draw the graph like this:

We have to basically find the area of ABCD

$$\triangle\ OAB$$ is a right angled triangle

Area of $$\triangle\ OAB=\dfrac{1}{2}\times\ OA\times\ OB=\dfrac{1}{2}\times\ 2\times\ 3=3$$ square units

Now we can see, ABCD is made by four such triangles $$\triangle\ OAB,\triangle\ OBC,\triangle\ OAD$$ and $$\triangle\ ODC$$

So, area of square ABCD = $$4\times\ 3$$ = $$12$$ square units.