A multiple of 12 is automatically a multiple of 6, so all you need to think of is multiples of 12.
2-digit multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96
Of all the 2-digit multiples of 12 listed above, only two have a sum of digits equaling 9: 36 and 72.
36 is a factor of 108 since 36 * 3 = 108.72 is not a factor of 108.
Answer: The number is 36.
