The two smaller triangles are similar to each other and to the larger one.
.. 12/x = x/6 . . . . . ratio of long leg to short leg
.. x^2 = 6*12
.. x = 6√2
.. y/12 = 18/y . . . . . ratio of hypotenuse to long leg
.. y^2 = 12*18
.. y = 6√6
In summary,
x = 6√2
y = 6√6