A two digit number is such that the product of the digits

is 8. When 18 is added to the number, the digits are
reversed. Find the number.

Your choices are quite limited.

Since the digits have to be whole numbers, and
8 = 1x8 or 2x4

only 4 choices for the first condition are:
18, 81, 24, or 42

Which of these also matches the second condition of your problem?