Choice B is the correct answer.

1. Factor out the GCF of 3: $3(x^2 - 4) = 0$.
2. Divide by 3: $x^2 - 4 = 0$.
3. Factor difference of squares: $(x - 2)(x + 2) = 0$.
4. Solve: $x = 2$ or $x = -2$.

Alternatively, isolate $x^2$: $3x^2 = 12 \Rightarrow x^2 = 4 \Rightarrow x = \pm 2$.

Choice A is incorrect because it misses the negative solution. Choice C is incorrect because it forgets to take the square root of 4. Choice D is incorrect because it forgets to divide by 3 first.