Clarification Note:** Since \( \log_2(x^2 - 4) = 3 \) requires \( x^2 - 4 > 0 \Rightarrow x^2 > 4 \Rightarrow |x| > 2 \), both \( \pm 2\sqrt{3} \approx \pm 3.464 \) satisfy this. However, the equation yields \( x^2 = 12 \), so both roots are valid. Depending on context, both may be acceptable. For a single boxed answer, we list the positive one:

["Clarification: Solving ( \log_2(x^2 - 4) = 3 ) Requires Domain and Solution Verification", "When solving logarithmic equations like ( \log_2(x^2 - 4) = 3 ), it is essential to first consider the domain constraints to ensure the argument of the logarithm remains positive. Since the logarithm ( \log_b(A) ) is only defined when ( A > 0 ), we begin with the inequality:", "[ x^2 - 4 > 0 ]\n[ x^2 > 4 ]\n[ |x| > 2 ]\nThis means ( x < -2 ) or ( x > 2 ).", "Next, solve the equation by rewriting it in exponential form:", "[ x^2 - 4 = 2^3 = 8 ]\n[ x^2 = 12 ]\n[ x = \pm \sqrt{12} = \pm 2\sqrt{3} ]", "Approximating, ( 2\sqrt{3} \approx 3.464 ), which satisfy ( |x| > 2 ), so both solutions are within the valid domain. Although ( x = -2\sqrt{3} ) is negative, it still meets the domain requirement ( |x| > 2 ), making both roots mathematically valid.", "However, depending on the application or context—such as modeling physical quantities restricted to positive values—only the positive root may be accepted. Nonetheless, for completeness and equality, both ( 2\sqrt{3} ) and ( -2\sqrt{3} ) satisfy the equation.", "Final boxed answer (positive solution):\n[ \boxed{2\sqrt{3}} ]"]