$A, B, C, D, E,$
with $A>B,C>D,D>B,E>B$
. In how many possible ways could the candidates be ranked?

What can you say about the ordering (not necessarily the rank) of
$B,C,D?$

You deduced an ordering of
$B,C,D.$
In how many positions can you place$A?$

What about the number of positions for
$E$
with respect to$A,B,C,D?$

From the given inequalities, it can be deduced that
$C>D>B.$
As$A>B,$
this leaves$3$
positions that$A$
can be placed in. Since$E>B$
then regardless of the position chosen for$A$
there are$4$
possible positions for$E.$
Therefore, there are$3 \cdot 4=12$
possible ways.