Choice B is the correct answer.

1. Take the square root of both sides: $\sqrt{(x+4)^2} = \sqrt{0}$.
2. Simplify: $x + 4 = 0$.
3. Solve: $x = -4$.

Since 0 has only one square root (0), there is only one unique solution (a repeated root).

Choice A is incorrect because of a sign error. Choice C is incorrect because 0 does not have a negative square root. Choice D is incorrect because it sets $x=0$ instead of the expression.