Please help, i am stuck

We may make use of the rule that if N's digits add up to a multiple of 3, N is a multiple of 3.

Since 6+7+8+9=30, which is a multiple of 3, all such N will be multiples of 3. Therefore the number you are looking for is the ways to organize the digits in N, which is 4!=24.

it is incorrect but good try!

Hint:

Any integer is divisable by three if the its digits add up to a multiple of 3.     [sum of digits is a multiple of 2]

So what do you think the answer is?

You will have to work out 4 digit numbers, 3 digit numbers, 2 and 1 digit numbers all seperately.