Solve the equation.

To solve the equation

\[
\frac{2}{3} + \frac{1}{5}x - \frac{1}{4} = \frac{4}{5}x,
\]

let's first rearrange the equation to isolate all terms involving \(x\) on one side and constant terms on the other side.

1. Start by simplifying the equation:

\[
\frac{1}{5}x - \frac{4}{5}x = -\frac{2}{3} + \frac{1}{4}.
\]

2. Combine the \(x\) terms:

\[
\frac{1 - 4}{5}x = -\frac{2}{3} + \frac{1}{4}.
\]

This simplifies to:

\[
-\frac{3}{5}x = -\frac{2}{3} + \frac{1}{4}.
\]

3. Now we need a common denominator to combine the constants on the right side. The least common multiple of 3 and 4 is 12. Rewrite \(-\frac{2}{3}\) and \(\frac{1}{4}\):

\[
-\frac{2}{3} = -\frac{8}{12},
\]
\[
\frac{1}{4} = \frac{3}{12}.
\]

So we have:

\[
-\frac{3}{5}x = -\frac{8}{12} + \frac{3}{12}.
\]

Now combine the fractions on the right:

\[
-\frac{3}{5}x = -\frac{8 - 3}{12} = -\frac{5}{12}.
\]

4. Now we can multiply both sides by -1:

\[
\frac{3}{5}x = \frac{5}{12}.
\]

5. To isolate \(x\), multiply both sides by the reciprocal of \(\frac{3}{5}\), which is \(\frac{5}{3}\):

\[
x = \frac{5}{12} \cdot \frac{5}{3} = \frac{25}{36}.
\]

Thus, the solution to the equation is

\[
\boxed{\frac{25}{36}}.
\]