1. **State the problem:** Find the expression for the perimeter of a square table whose area is given by $$9x^4 - 24x^2 + 16$$. 2. **Recall the formulas:** - Area of a square: $$A = s^2$$ where $$s$$ is the side length. - Perimeter of a square: $$P = 4s$$. 3. **Find the side length $$s$$:** Since $$A = s^2 = 9x^4 - 24x^2 + 16$$, we need to find $$s = \sqrt{9x^4 - 24x^2 + 16}$$. 4. **Factor the area expression:** Notice that $$9x^4 - 24x^2 + 16$$ is a perfect square trinomial: $$9x^4 - 24x^2 + 16 = (3x^2 - 4)^2$$. 5. **Calculate the side length:** $$s = \sqrt{(3x^2 - 4)^2} = |3x^2 - 4|$$. 6. **Write the perimeter expression:** $$P = 4s = 4|3x^2 - 4|$$. **Final answer:** $$\boxed{4|3x^2 - 4|}$$