For 1x4 rectangles, the yellow ones, there are 10 of them (going horizontally)
For 4x1 rectangles, the blue ones, there are also 10 (going vertically).
For the 2x2 squares, the green ones, there are 16.
Add the cases up to get your answer.
I found these cases by handcounting every rectangle, but if you would like an algebra solution for problems like this with bigger numbers, I could explain that as well.