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 by green arrows. The "key information" that allows the correct solution to be found is probably the IR and 13C data (make sure you have a compound with only 3 types of C in the set), and the chirality information.

The important knowledge required to solve the problem is a strong knowledge of the reactions involved and definitions of terms.

A = cyclohexene
B = 3-bromocyclohexene
C = 2-cyclohexenol
D = 2-cyclohexeneone
E = cyclohexanone
F = cyclohexanol

I = D (6 different C including C=O and 2 sp² C from C=C), II = A (only 3 different C including 1 x sp² from a symmetrical C=C)

B is the major product of the reaction of A with Br₂ / uv light because bromine radical halogenations are highly selective for the more stable radical and the postion adjacent to the C=C gives a radical that is resonance stabilised.