Answer:
13 1/3
Explanation:
In order to find EF, you need to find the length of at least one other unmarked segment in triangle BFD. Easiest is BC, which you can find from the relations related to angle bisector AC.
That bisector creates proportional segments on either side, so ...
... BC/AB = CD/AD
... BC = AB×CD/AD = 18×16/24 = 12
Then the proportional relations hold in ∆BFD due to parallel segments EC and FD:
... BE/BC = EF/CD
... EF = CD×BE/BC = 16×10/12
... EF = 40/3 = 13 1/3