If sin theta = (sqrt 3)/2, which could not be the value of theta? a. 60 degrees b. 120 degrees c. 240 degrees d. 420 degrees i know that the solutions for theta are pi/3 and 2pi/3, but how does that correlate?

Your are right,  and 2 are solutions.
Of course each of these solutions can be replaced by the same number +k2 (with k being an element of Z) since sin x=sin (x+k2) with k being an element of Z. 
Those are angle measures expressed in radians.
If you translate in degrees you basically have to know that   radian=180 degrees
so  radian=60 degrees and 2=120 degrees. So this two could be values of theta (A and B).
On top of that  could also be a solution (x+k2 with k=1). This can be translated to 60+360=420 degrees which is solution D.
So C. 240 degrees is the only one that could not be a value of theta.

What is the rest of the question?