Getting wrong answer for absolute value inequality and not sure why

$20$ is greater than $8$, right?

$$20 > 8$$

Now divide both sides by $-2$:

$$-10 > -4$$

Whoops! That's not right. This is because when you multiply or divide an inequality by a negative number, you must change the sense of the inequality: $>$ becomes $<$, and $\le$ becomes $\ge$ etc:

$$-10 < -4$$

$-2|x+4|>-14$ implies that $|x+4|<7$ (the greater than becomes smaller than because you multiply by a negative number).

The rest is all good.