6 cos^{2} x = 3
Is that your question?
If so,
Divide both sides by 6:
(6 cos^{2} x)/6 = 3/6
cos^{2} x = 1/2
Take the square root of both sides:
cos x = +/- sqrt(1/2)
cos x = +/- (√2)/2
Cos x = +/- Sqrt(2)/2 at every multiple of pi/4
cos pi/4 = Sqrt(2)/2
cos 3pi/4 = - sqrt(2)/2
cos 5pi/4 = - sqrt(2)/2
cos 7pi/4 = sqrt(2)/2
...
So x = (pi)(2n+1)/4 for n = 0,1,2,3...
It depends on if they gave you an interval to use for the solution set.
For example, they could have said x or "theta" such that 0<= x <= 2pi.
If so, the answers would be x = {pi/4, 3pi/4, 5pi/4, 7pi/4}