Question

This is really confusing to me

Answer 1

Since it is given the point E is the midpoint of segment BD then we can also say that it is the midpoint of segment AC.

So since E is the midpoint we can set AE and EC equal to each other and solve for x.

AE = EC

6x - 15 = x + 30
6x = x + 45
5x = 45
x = 9

So the value of x is 9.

Hope this helps :)

Answer 2

One of the properties of parallelograms is that the diagonals must bisect each other, that means that each diagonal is divided into two equal parts by the point at which they cross (see picture).

Your diagonals are AC and BD, and they cross at point E. That means BE = DE (which you are told) and AE = EC for it to be a parallelogram. You're given that AE = 6x - 15 and EC = x + 30. Because they must be equal to create a parallelogram, set those values equal to each other and solve for x:
$AE = EC\\ 6x - 15 = x + 30\\ 5x = 45\\ x = 9$

x must equal 9 for ABCD to be a parallelogram.