Answer: \(x\lt2\) or \(x\gt6\).

Start by taking the key information from the graph or diagram, such as intercepts, turning points, amplitudes, periods, or intersection points. Then use the relevant algebra to justify the result.

For a graphical method, draw \(y=|2x-8|\) and \(y=4\).

The graph \(y=|2x-8|\) is a V-shape with vertex at \((4,0)\).

The line \(y=4\) intersects it where

\(|2x-8|=4\).

So \(2x-8=4\) or \(2x-8=-4\), giving \(x=6\) and \(x=2\).

The graph of \(y=|2x-8|\) is above \(y=4\) outside these two intersection points.

Therefore \(x\lt2\) or \(x\gt6\).

The result has been obtained using the exact condition from the question, so no additional solutions are introduced.