Answer
$(-4,-2)$
Work Step by Step
Step 1. Rewrite the inequality as $x^2+6x+8\lt0$
Step 2. Factor the quadratic, we have $(x+4)(x+2)\lt0$
Step 3. The boundary points are $x=-4$ and $x=-2$
Step 4. Use test points at $x=-5, -3, 0$, the signs of the quadratic are $+, -, +$
Step 5. The inequality requires negative, thus the solution interval (middle region) is $(-4,-2)$