#1**0 **

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**.

gb1falcon May 5, 2023