The area of the entire figure is 120m ^2. find the area of the shaded region.

Area = length * width. If the area is given as 120, and we have sides measuring (2x+1) and 8, those are the sides being muliplied together to give us a product of 120:  120 = (2x+1)8--> 120 = 16x + 8--> solving for x gives us 7. Now we sub in that value of 7 for the x's inside the smaller rectangle: 2(7-4) = 6 and 7+2=9. The area of the smaller rectangle is 6 * 9 = 54. Subtract that from the area of the whole thing to give you 120 - 54 = 66 (aka the shaded region).

If you make it a little more clear i can answer it