I think the rules are:
1) You pick any target number
2) Place your counter on a starting node and write down its number. This is your current total
3) Move the counter to any node which is connected to the current node by a line (except the node you just came from). Add the number of the node we move on to, to our current total
4) Keep going until you reach your target number
The winner is the player who can reach their target in the fewest moves
I think the best way to win is:
1) If our target is 6 or less, start on the node whose number is equal to our target, otherwise start on the node labelled 6.
2) If our target minus our current number is less than 6 then move to the node that gets to our target if possible, otherwise move to the node with the highest number which keeps you below the target
3) If our target minus our current number is 6 or more then move to the highest numbered node which we are allowed to move to