\[\left( x^{2} + 6x + 8 \right)^{2} < - x^{2} - 6x - 8\]
\[\left( x^{2} + 6x + 8 \right)\left( x^{2} + 6x + 9 \right) < 0\]
\[(x + 2)(x + 4)(x + 3)^{2} < 0\]
\[Ответ:( - 4; - 3) \cup ( - 3; - 2).\]