Lewis sent us his solution. He's explained each step very clearly.

Here are all the possible numbers:18, 86, 120, 42, 46, 64, 80, 8, 22, 83.

The number has two digits, so it can't be 120 or 8. So the possible numbers now are 18, 86, 42, 46, 64, 80, 22, 83.

Both of the digits are even, so the number can't be 18 or 83. So the possible numbers now are 86, 42, 46, 64, 80, 22.

The digit in the tens place is greater that the digit in the unit (or ones) place, so the number can't be 46 or 22. So the possible numbers now are 86, 42, 64, 80.

The units (or ones digit) is not in the three times table, so the number can't be 86. So the possible numbers now are 42, 64, 80.

The tens digit is not double the ones digit, so the number can't be 42. So it can only be 64 or 80.

The sum of the two digits is a multiple of five, so the number can't be 80, so it must be 64.