the two vertices given are on the x-axis
the distance between them is 12 units (-6 to 6 is 12 units)
using quadrant 1, form a right triangle with the positive part of the x-axis and the positive part of the y-axis being the legs of the right triangle
the hypotenuse must be 12 units because we have an equilateral triangle
using the Pythagorean Theorem...
12^{2}=6^{2}+y^{2} where y is the distance to the third vertex and therefore the y-coordinate of the third vertex
144=36+y^{2}
144-36=y^{2}
108=y^{2}
y^{2}=108
y=√108
y=√36*3
y=6√3
the third vertex is (0, 6√3) which is C.