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 sides2x+3y=6 and  2x+3y=−6Length of the diagonals is 6 and 4 units along x-axis andy-axis.∴ The required area =12×6×4=12 sq. units.