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
