Help with geometry

By the intersecting chords theorem,  

8*9  =  x *2x   ......simplify

72 = 2x^2       divide both sides by 2

36  = x^2       take the positive square root

6 = x

Applying the theorem again, we have

4 * y  =  x *2x

4 * y =  6 * 2(6)

4 * y   = 72       divide both sides by 4

y = 18