First, 12 is a multiple of 6, so we only need to look for multiples of 12. Also, it has to be smalle,r or equal to than 108 since it's its factor. So let's list the multiples of 12 smaller than 108:12,24,36,48,60,72,84,96,108. Of these only 36,72 and 108 have a sum of digits 9, but 108 is not a two digit number. 72 is not a factor of 108, but 36 is (if you multiply it by 3), so 36 is the correct answer!
