Solve the equation. \[ \frac{4}{10} x-4 x+\frac{8}{5}=\frac{4}{5} \]

To solve the equation \[ \frac{4}{10} x - 4 x + \frac{8}{5} = \frac{4}{5}, \] first simplify \(\frac{4}{10} x\) to \(\frac{2}{5} x\): \[ \frac{2}{5} x - 4 x + \frac{8}{5} = \frac{4}{5}. \] Next, express \(4 x\) as \(\frac{20}{5} x\) so that all terms have a common denominator: \[ \frac{2}{5} x - \frac{20}{5} x + \frac{8}{5} = \frac{4}{5}. \] Combining the \(x\) terms: \[ \left(\frac{2}{5} - \frac{20}{5}\right)x + \frac{8}{5} = \frac{4}{5}. \] This simplifies to: \[ -\frac{18}{5} x + \frac{8}{5} = \frac{4}{5}. \] Next, isolate the \(x\) term by subtracting \(\frac{8}{5}\) from both sides: \[ -\frac{18}{5} x = \frac{4}{5} - \frac{8}{5}. \] This simplifies to: \[ -\frac{18}{5} x = -\frac{4}{5}. \] Now, multiply both sides by \(-\frac{5}{18}\) to solve for \(x\): \[ x = -\frac{4}{5} \cdot -\frac{5}{18} = \frac{4}{18} = \frac{2}{9}. \] Thus, the solution to the equation is \[ \boxed{\frac{2}{9}}. \]