1. **State the problem:** We are given the quadratic function $$p(x) = x^2 + 8x + 12$$ and the solutions for $$x$$ as $$x = -4 \pm 2$$. 2. **Recall the quadratic formula and factorization:** The quadratic formula for roots of $$ax^2 + bx + c = 0$$ is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. Alternatively, we can factor the quadratic if possible. 3. **Factor the quadratic:** $$p(x) = x^2 + 8x + 12 = (x + 6)(x + 2)$$ because $$6 \times 2 = 12$$ and $$6 + 2 = 8$$. 4. **Find the roots by setting each factor to zero:** $$x + 6 = 0 \Rightarrow x = -6$$ $$x + 2 = 0 \Rightarrow x = -2$$ 5. **Check the given solution $$x = -4 \pm 2$$:** Calculate $$-4 + 2 = -2$$ and $$-4 - 2 = -6$$, which matches the roots found by factoring. 6. **Conclusion:** The roots of the quadratic function $$p(x) = x^2 + 8x + 12$$ are $$x = -6$$ and $$x = -2$$, confirming the given solution. **Final answer:** $$x = -4 \pm 2$$ or equivalently $$x = -6$$ and $$x = -2$$.