Spectroscopy

Oh no! You, Harry, Ron, Hermoine, Ben, and Professor Koreeda are trapped in the Devil's Snare, a trap set by Professor Sprout to prevent further progress towards the Sorcerer's Stone. If you keep struggling, it will suffocate you! In order to prevent it from doing further harm to you and your friends, you must enlighten yourself using the spectroscopy below! Good luck!

snare

Hydrogen #1 is the furthest peak downfield due to its attachment to the double-bond and because it is fairly close to two oxygen atoms which help to deshield the hydrogen molecule. Additionally, the resonance structure of molecule #6 can create a carbocation to which this hydrogen is bonded.
Hydrogen #2 is the next peak upfield at about 6.17 ppm. This peak is located where it is on the HNMR spectra because of its attachment to the double bond.
Hydrogen #3 is the next peak upfield at about 5.64 ppm. This hydrogen is at this position because it is attached to a carbon that is attached to two other oxygen atoms. These oxygen deshield this hydrogen atom, thus moving it further downfield.
Hydrogen #4 is the next peak upfield at about 4.58 ppm. This hydrogen is deshielded by the two oxygen atoms that are closely attached to it. Also, the resonance structure created by moving the double-bond electrons to the oxygen creates a carbocation which adds to the deshielding effect. In addition, this carbon is further downfield than the other hydrogen bonded to the same carbon because it is cis to the alcohol group on the ring.
Hydrogen #5 is the next peak upfield at about 4.14 ppm. This hydrogen is deshielded in the same ways as hydrogen #4, but since it is trans with the alcohol group, it is further upfield.
Hydrogen #6 is the furthest peak upfield at about 3.26 ppm. This hydrogen is deshielded by the oxygen it is directly bonded with.
Other peaks are not associated with molecule #6.

Shimokawa, J.; Harada, T.; Yokoshima, S.; Fukuyama, T. J. Am. Chem. Soc. 2011, 133, 17634-17637.