6. AB AC AD AE AF
5 ways
If you used AB, then, there would be 4 remaining ODD vertices (C, D, E and F) CD CE CF
3 ways
If you used CD, then, there would be 2 remaining ODD vertices (E and F) EF
1 way

7. Here are the 15 ways
AB BC CD DE EF
AC BD CE DF
AD BE CF
AE BF AF

9. A B C D E F G H

21. What the examiner is looking for
You have stated the ODD VERTICES
You have stated the different combinations and their distances
You have stated which combination is repeated
You have added the new edges to your diagram
You have stated the total distance, showing the sum