Answer: x-intercepts \((-2,0)\), \((1,0)\), \((6,0)\), y-intercept \((0,-12)\); \(-2\leq x\leq1\) or \(x\geq6\).

(a) The graph meets the \(x\)-axis when

\(-(x+2)(x-1)(x-6)=0.\)

Thus

\(x=-2,\quad x=1,\quad x=6.\)

So the \(x\)-intercepts are

\((-2,0),\quad (1,0),\quad (6,0).\)

The y-intercept is found by putting \(x=0\):

\(y=-(2)(-1)(-6)=-12.\)

So the graph meets the y-axis at \((0,-12)\). The leading term is \(-x^3\), so the curve rises to the left and falls to the right.

(b) From the sketch or sign analysis, the expression is non-positive between \(-2\) and \(1\), including both endpoints, and for \(x\geq6\).

Hence

\(\boxed{-2\leq x\leq1\quad\text{or}\quad x\geq6}.\)