Solve the equatioin `|x-|4-x||-2x=4`

Explanation

The equation is equivalent to the collection of systems
`{(|x-(4-x)|-2x=4, "if"4-xge0),(|x+(4-x)|-2x=4, "if"4-xlt0):}`
`implies {(|2x-4|-2x=4, "if"xle4),(4-2x=4,"if"xgt4):}`……I
The second system of this collection gives `x=0`
but `xgt4`
Hence, second system has no solution.
The first system of collection Eq. (i) is equivalent to the system of collection
`{(2x-4-2x=4, "if"2xge4),(-2x+4-2x=4,"if"2xlt4):}`
`implies{(-4=4,"if"xge2),(-4x=0,"if"xlt2):}`
The first system is failed and second system gives `x=0`.
Hence `x=0` is unique solution of the give equation.