Thank you! :D
Here's the system's explanation:
We start by converting part-to-part ratios into part-to-whole ones. We know that $CE:EA=2:3$ and $AD:DB=4:5$, so $AE:AC=3:5$ and $AD:AB=4:9$.
Consider $\triangle ABC$. On the one hand, $\triangle ACD$ and $\triangle ABC$ share a height, so $\dfrac{[ACD]}{[ABC]}=\dfrac{AD}{AB}=\dfrac{4}{9}$. On the other hand, $\triangle ABE$ and $\triangle ABC$ share a height, so $\dfrac{[ABE]}{[ABC]}=\dfrac{AE}{AC}=\dfrac{3}{5}$.
Therefore, $\dfrac{[ACD]}{[ABE]}=\dfrac{(4/9)[ABC]}{(3/5)[ABC]}=\dfrac{4\cdot 5}{9\cdot 3}=\boxed{\dfrac{20}{27}}$.
