Find the missing length indicated. Leave your answer in simplest radical form.

The correct answer is: 9

Assuming the triangles formed with sides x and 12 be 1st  triangle, the triangle formed with sides 12 and 16 be the 2nd triangle and the bigger triangle be 3rd triangle.
In 1st triangle, we get :
let the length of the missing side be a

In 3rd triangle, we get :
let the length of the missing side be b

In 3rd triangle, we get :

so, the required value of x is 9.