How do you make multiples of 6 using 0-9 only once?

Answer 1

Here are two solutions: 1234567890 and 9876543210. There are many more.

To be a multiple of 6, the number must be both a multiple of 3 and a multiple of 2. If the sum of the digits is a multiple of 3, then the number is a multiple of 3. Adding up all digits (0 through 9) gives a sum of 45, which is a multiple of 3. Since addition is commutative, rearranging the digits in any order will still have a sum of 45, so it's still a multiple of 3. For it to be a multiple of 2, the last digit (the one's place) must be {0,2,4,6, or 8}