1. **State the problem:** Factor the expression $$9x^2 - 16$$ completely. 2. **Recognize the form:** This is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Identify squares:** Here, $$9x^2 = (3x)^2$$ and $$16 = 4^2$$. 4. **Apply the difference of squares formula:** $$9x^2 - 16 = (3x)^2 - 4^2 = (3x - 4)(3x + 4)$$. 5. **Final answer:** The completely factored form is $$\boxed{(3x - 4)(3x + 4)}$$.