Since 8 is an even number all multiples of 8 must be even, so each number divisible by 8 must end in 2, the only even digit in the set.
If we now combine each of the remaining four digits we get:
12=4×3, 32=4×8, 52=4×13, 72=4×18.
We need all the odd multiples of 4: 12 and 52.
Since all the remaining digits are odd, the following six 3-digit numbers are divisible by 8:
312, 512, 712, 152, 352, 752.
The remaining two digits can now prefix these six in either order:
57312, 75312, 37512, 73512, 35712, 53712, 37152, 73152, 17352, 71352, 13752, 31752 (12 numbers in all).