Answer
$BC=8 \ m$
Work Step by Step
Since ED and BC are parallel, then we have $\angle B=\angle E$ and $\angle C=\angle D$ and $\angle A$ is the common angle. Hence, the triangle AED is similar to the triangle ABC and hence
$$
\frac{AE}{AB}=\frac{ED}{BC} \Longrightarrow \frac{4}{8}=\frac{4}{BC} \Longrightarrow BC=8 \ m
.$$
