The area enclosed by 2|x|+3|y|≤6 is

The given inequality is equivalent to the following system of inequalities. 2x+3y≤6, when x≥0,y≥02x−3y≤6, when x≥0,y≤0−2x+3y≤6, when x≤0,y≥0−2x−3y≤6, when x≤0,y≤0which represents a rhombus with sides 2x±3y=6 and 2x±3y=−6The lengths of the diagonals are 6 units and 4 units, respectively, along the x- and y-axes. Therefore, the required area is (1/2) x 6 x 4 = 12 sq. units.