Answer
$ED = 12$
$FD = 24$
Work Step by Step
Theorem 6-7 states that if three or more parallel lines cut off congruent segments off of a transversal, then they will cut off congruent segments off of any transversal.
We see from the diagram that the transversal $\overline{AC}$ is cut off in equal segments by the three parallel lines. We can then deduce that line $DF$ is also a transversal that is cut off in congruent segments by the same three parallel lines. We now know that $ED$ is congruent to $FE$, so they both have a length of $12$.
We are asked to find the length of $\overline{FD}$. We can do this by adding the lengths of the two segments together:
$FD = FE + ED$
Let's plug in what we know:
$FD = 12 + 12$
Add to solve for $FD$:
$FD = 24$
