\(\left|2x-6\right|=3-x\)
\(\Rightarrow\left[{}\begin{matrix}2x-6=3-x\\2x-6=-\left(3-x\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x-6=3-x\\2x-6=-3+x\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x+x=3+6\\2x-x=-3+6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}3x=9\\x=3\end{matrix}\right.\)
\(\Rightarrow x=3\)