Now, that is a fairly long winded way of working out the answer, but it is the most fundamental and reliable. There is a shortcut, if what follows here confuses you, stick to the above.
I will call the carbon centre with the Br substituent C1, and the centre with the F C2.
If we compare the staggered structure in the original question part A with the Fischer projection (1), we can see that C1 matches up ok, and it is C2 that is different. The C1 centres in part A are assigned as
S (according to the
CIP rules).
Look at the staggered structures in A, B, and C. The configuration at C1 is
S in all cases. We worked out in part A that in the Fischer projection C1 has the
S configuration if the OH at C1 points to the
right.
We know A is incorrect (because the structures differ at C2) and in B and C both staggered structures have
S configuration at C1, however the OH's at C1 in the fischer projections for B and C point
left, and so must be
R. So we quickly spot that in B and C the structures differ
at least at C1, and B and C must be incorrect.
By process of elimination D is the answer. This saves alot of drawing.