Three circles must be placed at each vertex and the remaing three circles must be placed at the centre of each side. So if the triangle is ABC, then there are three circles each containing a number A, B and C, and there are three circles D, E and F such that D is on AB, E on BC and F on CA.
Only the numbers 1 to 6 can be used for A to F. The numbers 1 to 8 can be split into 4 pairs: so that the sum is 9: (1,8), (2,7), (3,6), (4,5) and the larger number can be further split: (1,2,6), (1,3,5), (2,3,4). Where we have the same number in common in these groups of three we order them so that the common number is at the beginning or end: (1,6,2), (2,4,3), (3,5,1). That gives us the numbers we need, because A=1, B=2 and C=3 and D=6, E=4 and F=5.