I am going to assume that you must use each digit exactly once. You have 6 choices for the units digit, leaving 5 choices for the tens digit, leaving 4 choices for the hundreds digit, and so on. In all, 6*5*4*3*2*1 different numbers.
How many of these six digit numbers are divisible by six?
A number is divisible by six if and only if it is divisible by 3 and it is even (that is, divisible by 2). What is the criterion for divisibility by 3? Is it preserved when you permute the digits? What is the criterion for divisibility by 2? How many choices does that leave for the units digit?Cheers,
Claude and Denis