Using only the digits 2, 3 and 9, how many six digit numbers can be
formed which are divisible by 6?

If a number is divisible by 6, then it should be divisible by 2 and 3 both, and divisibility rule of 3 is, if the sum of digits is divisible by 3 then number will be divisible by 3. In this case sum of digits is 14 which is not divisble by 3, hence there is no number exists which is divisible by 3. So answer is zero.