Given a triangle with a=6, A=33, and B=30, what is the length of c?

Angle C is 180 deg - 63 deg = 117 degrees.
Then use the Law of Sines:
c/sin(117) = a/sin(A) = 11.016
c = 11.016*sin(117) = 9.816

Do you mean that one side has length 6, the opposite angle is 33 DEGREES, and another angle is 30 DEGREES.

The units are very important! Angles are not always measured in degrees. You can have radians, grads, arc-minutes and arc-seconds, and other units for angles.

If I tell you that c = 10, how will you know if that is right or wrong, since you don't know how to do it yourself?