Analyze the diagram below and complete the instructions that follow.

The large triangle is isosceles, so that the two smaller triangles that appear inside the large one have bases of 12/2, or 6.

Let's see how x and y are related:

sin 60 degrees = opp/hyp = x/y = sqrt(3) / 2

and  cos 60 degrees = adj/hyp = 1/2 = 6 / y.  Then y = 12 (which should be no surprise, since the large triangle is equilateral).  

Then:  x/y = sqrt(3) / 2, or

 x        sqrt(3)       x
= = , so that 2x = 12sqrt(3), or x=6sqrt(3).
  y           2           12

In summary, 
x = 6√3
y=12