6. Given the function $f(x)=|| x-1|-1|$, if the equation $f(x)=m(m \in \mathbf{R})$ has exactly 4 distinct real roots $x_{1}, x_{2}, x_{3}, x_{4}$, then the range of $x_{1} x_{2} x_{3} x_{4}$ is $\qquad$ .
6. $(-3,0)$.

The graph of the function $f(x)=|| x-1|-1|$ is shown in Figure 2. From the graph, we can see that if $f(x)=m$ has 4 distinct real roots, then $m \in(0,1)$, and the 4 roots are $m, 2-m, m+2, -m$. Therefore,
$$
x_{1} x_{2} x_{3} x_{4}=-m^{2}(2-m)(m+2)=\left(m^{2}-2\right)^{2}-4 \in(-3,0) \text {. }
$$