Explanation

Let's denote the original two-digit number as 10a + b.

Since the product of the digits is 8:

ab = 8

Possible values for a and b are (1, 8) or (2, 4).

When 18 is added to the number, the digits are reversed:

10a + b + 18 = 10b + a

Simplify the equation:

9a - 9b = -18

a - b = -2

Now, check the possible values:

For (1, 8): 1 - 8 ≠ -2 (not valid)

For (2, 4): 2 - 4 = -2 (valid)

So, the original number is 10(2) + 4 = 24.