What is the value of x in the diagram?

The triangle on the left is a 30-60-90 right triangle

The side oppsite the 30° angle  (in this case, the altitude of both triangles)  = 

(1/2) (hypotenuse )  = (1/2)(2√3)  =  √3

Now... the triangle on the right is a 45-45-90 right triangle....with both legs = √3

So....using the Pythagorean Theorem,  x  =  √ [ (√3)^2 + (√3)^2 ]  = √ [ 3 + 3 ]  =  √6