The equations that are true for x = -2 and x = 2 are x^2 - 4 = 0 and 2(x - 2)^2 = 0.
For x = -2, the equation x^2 - 4 = 0 becomes (-2)^2 - 4 = 0, which simplifies to 4 - 4 = 0, and therefore this equation is true when x = -2.
Similarly, for x = 2, the equation 2(x - 2)^2 = 0 becomes 2((2 - 2)^2) = 0, which simplifies to 2(0)^2 = 0, and therefore this equation is also true when x = 2.
The other equations, x^2 = -4, 3x^2 + 12 = 0, and 4x^2 = 16, are not true for x = -2 or x = 2. For example, for x = -2, the equation 3x^2 + 12 = 0 becomes 3(-2)^2 + 12 = 0, which simplifies to -24 + 12 = -12, and therefore this equation is not true when x = -2. Similarly, for x = 2, the equation 4x^2 = 16 becomes 4(2)^2 = 16, which simplifies to 16 = 16, and therefore this equation is true when x = 2. However, since the problem asks for equations that are true for both x = -2 and x = 2, the equation 4x^2 = 16 is not a correct answer because it is only true when x = 2.