ABC is an equilateral triangle.
Angle(DAB)=Angle(EBD)
Area(ABC)=7squareroot(3)
AE=4
|BE|=X=?
No one asked you to solve it. You were asked to show what work you have done and to explain where you get stuck. You have not even attempted these problems. If you have 99 other problems to do, then after you finish those, attempt this one, and get back to us. When you explain where you are having difficulty, we can help you.
You need to study this.
The area of an equilateral triangle, as you can see, is $\dfrac{\sqrt{3}s^2}{4}$ where $s$ is the length of a side.
Using the given: $\|\overline{BC}\|=s=2\sqrt{7}$.
SHOW SOME WORK!