Answer
$[-4,2)$.
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow -6\leq\frac{x}{2}-4\lt-3$
Multiply the inequality by $2$.
$\Rightarrow -12\leq x-8\lt-6$
Add $8$ to the inequality.
$\Rightarrow -12+8\leq x-8+8\lt-6+8$
Add like terms.
$\Rightarrow -4\leq x\lt2$
The interval notation is
$[-4,2)$.
