Answer
$x\lt -3$ or $(-\infty,-3)$
Work Step by Step
Step 1. Graph the left side $y_1=-2(x+4)$ as shown in the figure (red line).
Step 2. Graph the left side $y_2=6x+16$ as shown in the figure (green line).
Step 3. The intersect can be found at $(-3,-2)$
Step 4. For the red line to lie above the green line $y_1\gt y_2$, we have $x\lt -3$ or the interval $(-\infty,-3)$
