Identifying protons in NMR using the J values When looking over an old organic midterm I came across this question.

 

As you can see I got half of it right, but honestly I'm not sure how I got that one right or how you would answer this in general.  Looking back at this now it appears that the first signal was split into a doublet and each peak was then split into a triplet, which makes sense for proton c (first split by b and then by d).

The second one seems trickier.  It looks as though the signal was split into a quartet, and then each peak into a triplet.  To me that looks like it should be d - split into the quartet by e and then split into the triplets by c and b.  So why is the answer b?  These J values wouldn't have been supplied for now reason - is there a way I could have used them?  More generally, is it possible (and if so how) to identify the type of proton and the structure of a molecule if you just had access to the NMR and the J values like this?
The proton(s) in question absorbs at 5.95 ppm, the olefinic region - so it cannot be D which is expected to absorb upfield in the aliphatic region.  B is the correct answer.  Proton B would be split by proton C into a doublet with a 15.5 Hz separation (the coupling constant $\ce{J_{BC}}$).  Each line in the doublet would be further split into another doublet with a J=8 Hz spacing by proton A.  So now we have 4 lines, a doublet of doublets.  Each of these four lines will be further split into a triplet with 1.5 Hz spacing by the two (hence the triplet) D protons.

Using the chemical shift of a proton and the observed splitting (e.g. the coupling constants, or J values) can go a long way in helping to determine a structure, particularly in relatively simple molecules.  As molecules get more complicated you can do advanced experiments to help with the structure determination.  One example would be spin decoupling experiments.  For example, if we "know" which signal is due to the D protons, we could irradiate them with energy during our nmr experiment.  If they are coupled to proton B (they are), then the triplet in the B signal should diappear and we would just see our doublet of doublets.  This type of experiment confirms which protons are coupled to which other protons.  There are many other advanced nmr techniques that can be used to help in structure elucidation.