for x needs to be greater than or equal to 0 degrees but less than or equal to 360 degrees
Just like in algebra, you want to get the variable, x, by itself.
First, then, add sqrt(3) to both sides, effectively moving it to the right hand side.
Now, divide by 2.
This should leave sin(x) on one side and sqrt(3)/2 on the other. Now, you just have to think about where, from 0 to 360 degrees, sin(x) is equal to sqrt(3)/2. It's handy at this point to have your basic trig tables memorized, i.e., that you know the values for all your trig functions at common angles like 0, 30, 45, 60, and 90 degrees and also how to use those values along with the concept of references angles to find the "equivalents" of these angles all around the unit circle.
I'll leave that part to you, since it's memorization (or consulting tables).
$\displaystyle 2\;sin\;x - \sqrt{3} = 0$
$\displaystyle 2\;sin\;x = \sqrt{3}$
$\displaystyle sin\;x = \frac{\sqrt{3}}{2}$
$\displaystyle x = sin^{-1}\left(\frac{\sqrt{3}}{2}\right)\Longrightarrow x = \frac{\pi}{3},\;\frac{2\pi}{3},\;\frac{4\pi}{3},\; \frac{5\pi}{3}$