6. A function is called a "good function" if and only if it satisfies:
(1) It is defined on $\mathbf{R}$;
(2) There exist $a<b$, such that it is monotonically increasing on $(-\infty, a)$ and $(b, +\infty)$, and monotonically decreasing on $(a, b)$.
Then the following functions that are good functions are $\qquad$
(1) $y=x|x-2|$,
(2) $y=x^{3}-x+1$,
(3) $y=2 x^{3}-3 x^{2}-6 x-1$,
(4) $y=2 x^{7}+7 x^{4}+28 x+3$.
6. (1)(2)(3).
(1) $y=x | x-2$ | is monotonically increasing on $(-\infty, 1)$ and $(2,+\infty)$, and monotonically decreasing on $(1,2)$, satisfying the definition.
(2) $y=x^{3}-x+1$.
Notice that $y^{\prime}=3 x^{2}-1>0$
$\Leftrightarrow x \in\left(-\infty,-\frac{\sqrt{3}}{3}\right) \cup\left(\frac{\sqrt{3}}{3},+\infty\right)$.
Thus, $y=x^{3}-x+1$ is monotonically increasing on $\left(-\infty,-\frac{\sqrt{3}}{3}\right)$ and $\left(\frac{\sqrt{3}}{3},+\infty\right)$, and monotonically decreasing on $\left(-\frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3}\right)$, satisfying the definition.
(3) $y=2 x^{3}-3 x^{2}-6 x-1$.
Notice that $y^{\prime}=6 x^{2}-6 x-6>0$
$\Leftrightarrow x \in(-\infty, m) \cup(n,+\infty)$.
(Since $\Delta>0$, there exist $m$ and $n$ as the two real roots of $6 x^{2}-$ $6 x-6=0$ and $m0$ always holds.
Thus, $y=2 x^{7}+7 x^{4}+28 x+3$ is monotonically increasing on $\mathbf{R}$, not satisfying the definition.