Need help with certain puzzle

[beaver21]

Alright, so this is the second time I have come across this particular puzzle and it stumped me the first time, as well as the second.
I WAS able to come up with a solution, but that was purely from guessing. I know each puzzle is supposed to be able to be solved with no need to guess but I simply cannot figure this one out. The average time on this puzzle was about 1600 seconds. If you could help me out and let me know what it is I am missing, I would really appreciate it so I can get better at these!! Thank you

http://postimage.org/image/es63pnbjr/