#### Answer

Solution set: $[0,4]\cup[6,\infty)$

#### Work Step by Step

Follow the "Procedure for Solving Polynomial lnequalities",\ p.412:
1. Express the inequality in the form $f(x)<0, f(x)>0, f(x)\leq 0$, or $f(x)\geq 0,$
where $f$ is a polynomial function.
$x(4-x)(x-6) \leq 0$
$f(x)=x(4-x)(x-6)$
2. Solve the equation $f(x)=0$. The real solutions are the boundary points.
$x(4-x)(x-6)=0$
$x=0$ or $x=4$ or $x=6$
3. Locate these boundary points on a number line, thereby dividing the number line into intervals.
4. Test each interval's sign of $f(x)$ with a test value, $a$, from that interval,
$\begin{array}{llll}
Interval & a & f(a),signs & f(a) \leq 0 ? \\
& & a(4-a)(a-6) & \\
(-\infty,0) & -1 & (-)(+)(-) & F\\
(0,4) & 1 & (+)(+)(-) & T\\
(4,6) & 5 & (+)(-)(-) & F\\
(6,\infty) & 10 & (+)(-)(+) & T
\end{array}$
5. Write the solution set, selecting the interval or intervals that satisfy the given inequality. If the inequality involves $\leq$ or $\geq$, include the boundary points.
Solution set: $[0,4]\cup[6,\infty)$