11. Let $a \in \mathbf{R}$, the equation ||$x-a|-a|=2$ has exactly three distinct roots. Then $a=$ $\qquad$ .
11. 2 .

The original equation can be transformed into $|x-a|=a \pm 2$.
For the equation to have exactly three distinct roots, then $a=2$. At this point, the equation has exactly three distinct roots:
$$
\begin{array}{l}
x_{1}=2, x_{2}=6, x_{3}=-2 . \\
\text { Therefore, } a=2 .
\end{array}
$$