The area ( in square units) enclosed by 2|x|+3|y|≤6 is

We have 2|x|+3|y|≤6 This is equivalent to the following system of inequations:and, 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≤0These inequations form a rhombus having its diagonals of lengths 6 and 4 units, along the coordinate axesSo, required area =12(6×4)=12 sq. units