I hate math too, but years of stupid prep for tests made me get it, so I went ahead and solved the problem for you. I'll try to explain it...
N is the height; 2N is the width, since the rectangle is twice as wide as the height. The area is 2N<sup>2</sup> (N times 2N). This is area #1.
Here's the next rectangle, with 4 added to each side. Multiple the sides by each other (N + 4 times 2N + 4), and you get 2N<sup>2</sup> + 12N + 16.
Now the problem states that the rectangle with 4 added to each side is 88m<sup>2</sup> more than the original rectangle. So if we subtract the area of the first rectangle from the area of the second rectangle, we'll get 88m<sup>2</sup>. 2N<sup>2</sup> + 12N + 16 minus 2N<sup>2</sup> is 12N + 16. And since our answer is supposed to be 88m<sup>2</sup>, 12N + 16 = 88. Subtract 16 from both sides; you get 12N = 72. Divide by 12 on both sides, and N = 6. Now plug into the rectangles. On the first rectangle, you'll have a height of 6 (N) and a width of 12 (2N). On the second rectangle you'll have a height of 10 (N + 4) and a width of 16 (2N + 4).
Now to double check, multiply the height and width of the first rectangle to get 72, and multiply the height and width of the second rectangle to get 160. Subtract 72 from 160, and you get - surprise surprise - 88.
Hope that helped!