Question

How many six digit numbers are possible by using the digits 1, 2, 3, 4, 5, 6, 7 without repetition such that they are divisible by 12?

Answer 1

first of all take 6 no. at a time and check their sum as if it is divisible by 3 then arrange them so that their last 2 digit is divisible by 4 then the no is divisible by 12
ex.764312 and check permutation of remaining 4 in starting no.s

Answer 2

I hope you understood the concept.
(NOTE: this answer is for the condition when repetition of digits is not allowed.) as you did not state anything about repetition.

Do let me know if I am wrong.