The product of half my number times my number is 162. What is twice my number. Explain how you solved this problem ...

The factors that I found of 162 are:

1, 2, 3, 6, 9, 18, 27, 54, 81, 162

Out of those factors the only half of the listed factors that is also in that list is 9 (9 is half of 18) and ultimately 18 x 9 = 162.

So, since I now know that your number, I can now proceed to what you are asking.

18 x 2 = 36.

The final answer is 36.