We know that, in a triangle, all three of those interior angles will add up to 180 degrees. We can set up this equality:
2x + 2x + 6x = 180
And then solve for x
10x = 180
x = 18
We know that angle C is 2x, so substituting the value of x = 18, we find that angle C = 2(18) = 36 degrees