A schematic of the solution is shown below. The information from the question is given in black. Deductions directly from this information are given in red. Points that provide potential key information are shown in green which leads to the structures which are linked via the blue arrows to show the path required to work them all out. There are, of course, other possible thought pathways.

The crux to this problem is recognising the reagents and the implications for the functional groups in the starting materials and products of each step. Recognising the symmetry of D from the spectroscopic data is also important. Once D is determined, C, E, and F follow directly. C then gives B which in turn gives A. E allows access to H and also B, G is deduced from E and H from D. Note the how the symmetry and substitutent effects dictate the nitration reactions of D and E.

Common errors: (1) not being able to identify A as being a bromide from the MS (2) poor interpretation of the reactions (3) not recognising the symmetry (4) incorrect nitration of D and E.