How many rectangles have an area of 24cm squared?

Infinitely many.

Suppose the length of the rectangle is L cm where L >= sqrt(24) = 4.899 cm (approx).

Let the breadth of the rectangle be B = 24/L.

Then area = L*B = L*24/L = 24

Since there are infinitely many choices for L, there are infinitely many rectangles.

For example,

5 * 4.8

6 * 4

8 * 3

50* 0.48

60 * 0.4

600 * 0.04

6000 * 0.004

60000 * 0.0004 etc