Subtracting Fractions:
To subtract fractions, we need to have a common denominator. In this case, the common denominator is 10. Let's find the equivalent fractions for each fraction with a denominator of 10.

Converting Fractions:
- \( \frac{-2}{5} = \frac{-4}{10} \)
- \( \frac{-3}{10} = \frac{-3}{10} \)
- \( \frac{-4}{15} = \frac{-8}{30} \)

Subtracting Fractions:
Now that we have all fractions with a common denominator of 10, we can subtract them.
- \( \frac{-4}{10} - \frac{-3}{10} - \frac{-8}{30} \)
- \( \frac{-4 - 3 - 8}{10} \)
- \( \frac{-15}{10} \)

Simplify the Fraction:
Finally, we simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 5.
- \( \frac{-15 \div 5}{10 \div 5} \)
- \( \frac{-3}{2} \)
Therefore, the result of \( \frac{-2}{5} - \frac{-3}{10} - \frac{-4}{15} \) is \( \frac{-3}{2} \).