4. Present a method to simulate a random variable having distribution function

$$

\begin{aligned}

F(x) &= \begin{cases}

0 & x \le -3 \\

\frac{1}{2} + \frac{x}{6} & -3 < x < 0 \\

\frac{1}{2} + \frac{x}{32} & 0 < x \le 4 \\

1 & x > 4

\end{cases}

\end{aligned}

$$