To simplify the expression \(-\frac{4}{5} - \frac{2}{9} - \frac{4}{5} - \frac{2}{9}\), first, combine like terms. We have two instances of \(-\frac{4}{5}\) and two instances of \(-\frac{2}{9}\).

1. **Combine the \(-\frac{4}{5}\) terms:**
\[
-\frac{4}{5} - \frac{4}{5} = -\frac{8}{5}
\]

2. **Combine the \(-\frac{2}{9}\) terms:**
\[
-\frac{2}{9} - \frac{2}{9} = -\frac{4}{9}
\]

3. **Now add the two results together:**
\[
-\frac{8}{5} - \frac{4}{9}
\]

To add these fractions, we need a common denominator. The least common multiple of 5 and 9 is 45.

4. **Convert \(-\frac{8}{5}\) to have a denominator of 45:**
\[
-\frac{8}{5} = -\frac{8 \times 9}{5 \times 9} = -\frac{72}{45}
\]

5. **Convert \(-\frac{4}{9}\) to have a denominator of 45:**
\[
-\frac{4}{9} = -\frac{4 \times 5}{9 \times 5} = -\frac{20}{45}
\]

6. **Now combine the two fractions:**
\[
-\frac{72}{45} - \frac{20}{45} = -\frac{72 + 20}{45} = -\frac{92}{45}
\]

Thus, the simplified result of the expression \(-\frac{4}{5} - \frac{2}{9} - \frac{4}{5} - \frac{2}{9}\) is

\[
-\frac{92}{45}
\]