1. The problem is to solve the equation $|x| = 2$. 2. Recall that the absolute value $|x|$ represents the distance of $x$ from zero on the number line, so $|x| = a$ means $x = a$ or $x = -a$ for $a \geq 0$. 3. Applying this rule to $|x| = 2$, we get two cases: $$x = 2$$ and $$x = -2$$ 4. These are the two solutions to the equation. 5. Therefore, the solution set is $\boxed{\{2, -2\}}$. This means $x$ can be either 2 or -2 to satisfy the equation $|x| = 2$.