Counting

We can use casework to solve this question.

1*1 rectangles: 12

1*2 rectangles: 9

1*3 rectangles: 6

1*4 rectangles: 3

2*1 rectangles: 8

2*2 rectangles: 6

2*3 rectangles: 4

2*4 rectangles: 2

3*1 rectangles: 4

3*2 rectangles: 3

3*3 rectangles: 2

3*4 rectangles: 1

So, the answer to this question is 12+9+6+3+8+6+4+2+4+3+2+1=60.