\(\dfrac{1}{3}\left|-2x+4\right|=x+3\\ \left|-2x+4\right|=\left(x+3\right):\dfrac{1}{3}\\ \left|-2x+4\right|=3\cdot\left(x+3\right)\\ \left|4-2x\right|=3x+9\\ \Rightarrow\left[{}\begin{matrix}4-2x=3x+9\\2x-4=3x+9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}-3x-3x=9-4\\2x-3x=4+9\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}-6x=5\\-x=5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{5}{6}\\x=-5\end{matrix}\right.\)