To calculate this, we first need to "find" the area of both shapes: the big rectangle and the small rectangle.
4x * (x + 2) = 4x^2 + 8x
x * (3x + 5) = 3x^2 + 5x
[ shaded area ] = [ big rectangle area ] - [ small rectangle area ]
This is 4x^2 + 8x - (3x^2 + 5x) = 4x^2 + 8x - 3x^2 - 5x = x^2 + 3x