List the critical values of the related function. Then solve the inequality.
$$\frac{4x}{x+6}\ge 0$$
The critical value(s) is/are
(Simplify your answer. Type an integer or a simplified fraction. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

Step 1 ：The critical values of a function are the values of x that make the function equal to zero or undefined. In this case, the function is undefined when the denominator is zero, i.e., $x=-6$. The function is zero when the numerator is zero, i.e., $x=0$. So, the critical values are $x=-6$ and $x=0$.

Step 2 ：To solve the inequality, we need to consider the intervals determined by the critical values and test a value in each interval. The intervals are $(-\mathrm{\infty },-6)$, $(-6,0)$, and $(0,\mathrm{\infty })$.

Step 3 ：The critical values are $x=0$ and $x=-6$. The inequality holds for the intervals $(-\mathrm{\infty },-6)$ and $(0,\mathrm{\infty })$.

Step 4 ：Final Answer: The critical values are $\boxed{{\displaystyle -6,0}}$. The solution to the inequality is $\boxed{{\displaystyle x<-6,x>0}}$.