To solve the equation \( m^2 - 4 = 0 \), we can start by adding 4 to both sides:
\[ m^2 = 4 \]
Next, we take the square root of both sides. Remember that taking the square root introduces both a positive and a negative solution:
\[ m = \pm \sqrt{4} \]
Since \( \sqrt{4} = 2 \), we have:
\[ m = 2 \quad \text{or} \quad m = -2 \]
Thus, the solutions are:
\[ m = 2 \quad \text{or} \quad m = -2 \]