Subtract 4 from all parts of the inequality.

$$-11 - 4 \le 4 - 3x - 4 \le 28 - 4$$ $$-15 \le -3x \le 24$$

Remember to reverse the inequality signs when dividing by a negative number.

$$\frac{-15}{-3} \ge \frac{-3x}{-3} \ge \frac{24}{-3}$$ $$5 \ge x \ge -8$$

$$-8 \le x \le 5$$

Comparing this result with the given options:
A. $-5 \le x \le 8$
B. $5 \le x \le 8$
C. $-8 \le x \le 5$
D. $-5 < x \le 8$

The correct option is C.

The final answer is $\boxed{\text{C. -8 \le x \le 5}}$.