Find the measure of each angle of triangle abc, given ac=6, cb= 2 square roots of 3, and ab= 4 square roots of 3

Note that 
(4sqrt3)^2 = (2sqrt3)^2 + 6^2     [ 48  =   12 + 36]  so the triangle is  a right angled one with hypotenuse AB 

So angle C = 90 degrees

sin A =   2 sqrt3 / 4 sqrt3 = 1.2  giving A = 30 degrees
and B = 90 - 30 = 60 degrees

A = 30, B = 60 and C = 90 degrees