In the given triangle ABC The side AC is parallel to DE.
From the Basis Proportionality theorem,
[tex]\begin{gathered} \frac{BD}{BA}=\frac{BE}{BC} \\ \frac{3}{4}=\frac{BE}{6} \\ BE=\frac{6\times3}{4} \\ BE=4.5 \end{gathered}[/tex]Thus, the requried value of BE is 4.5.
