1. The solution to the equation $x=|x-| x-6||$ is $x=$
1.2, 6.
If $x \geqslant 6$, then the solution to the equation is $x=6$. If $x<6$, the equation becomes $x=|2 x-6|$.
(1) When $3 \leqslant x<6$, the equation has no solution;
(2) When $x<3$, the equation has a solution $x=2$.
Therefore, the solutions to the original equation are $x=2,6$.