To solve the equation
\[ \frac{4}{5} n - \frac{1}{5} = \frac{2}{5} n, \]
we can start by eliminating the fractions. We can multiply the entire equation by 5 to clear the denominators:
\[ 5 \left( \frac{4}{5} n \right) - 5 \left( \frac{1}{5} \right) = 5 \left( \frac{2}{5} n \right). \]
This simplifies to:
\[ 4n - 1 = 2n. \]
Next, we'll isolate the terms involving \(n\). To do this, we can subtract \(2n\) from both sides of the equation:
\[ 4n - 2n - 1 = 0. \]
This combines to:
\[ 2n - 1 = 0. \]
Now, we add 1 to both sides:
\[ 2n = 1. \]
Finally, we divide both sides by 2:
\[ n = \frac{1}{2}. \]
Thus, the solution to the equation is
\[ \boxed{\frac{1}{2}}. \]