First think of the Br, D, OH as being able to rotate about the chrial carbon.
Rotate Br, D, OH so that Br is in the back. (Mentally carry D toward the left.)
That way, D is on the left (towards you), Br is in the back (away from you), and OH is to the right (also towards you). Draw out the stick version.
(Remember: horizontal lines are towards you....if you have a hard time remember....think of them as bow ties, or that they look like hands which are out to huge you.)
Next, do the same for the bottom part. The way it's drawn OH is already in the back. So simply translate into Fisher. F to the right, H to the left, OH on the bottom.
So combine and draw Fisher.
The way I decribed, it looks like...
Br on top
D to left
OH to right
H to left
F to right
OH on bottom
Now, one important thing to remember about Fischer projections is that you can switch around the elements on the chiral carbon. Things that are next to each other can be switched. Example, if we switch the Br and the D, the Fisher we get is an enanitomer. But, if we carry out another switch, then we get a different representation of the original Fisher. For example, if you carry out a switch between the Br and top OH. This Fisher would be the same as the original Fisher.
So the key is: 1 switch = Enantiomers, 2 switches: Identical.
For us to get the Fisher to look like the one showen next to A...we'd have to carry out 1 switch between the F on the right and the bottom OH. Thus, the Fisher drawn in A is an enantiomer of the true Fisher, thus it is not the correct answer.