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 which leads to the structures which are linked via the blue arrows to show the path required to work them all out. The "key information" that allows the correct solution to be found is that F is an alkene with only 2 types of C, this gives E and then D from which the others are deduced. D reacts with HBr via SN1 reaction hence the rearrangement.
There are, of course, other possible thought pathways.