Let's analyze the mathematical expression shown in the image:

1. The expression begins with two main parts on the left-hand side: $-4 \times \frac{2}{15} + 4 \times \frac{2}{15}$

2. This is simplified as: $-\frac{8}{15} + \frac{8}{15} = 0$

   So, the first part simplifies to $0$.

3. Then, the next line seems to show another subtraction: $-\frac{2 \times 9}{15}$

4. Simplifying $2 \times 9 = 18$, so: $-\frac{18}{15} = -\frac{6}{5} = -1\frac{1}{5}$

5. The final step adds: $1\frac{8}{15} - 1\frac{1}{5}$

6. Converting $1\frac{1}{5}$ to a fraction with the denominator 15: $1\frac{1}{5} = 1\frac{3}{15}$

7. Thus, the result is: $1\frac{8}{15} - 1\frac{3}{15} = \frac{5}{15} = \frac{1}{3}$

So, the final answer is $\frac{1}{3}$.

Would you like further details or have any questions about this solution?

Here are five related questions for practice:

1. How do you simplify fractions with different denominators?
2. What is the process for multiplying fractions?
3. How can you convert an improper fraction to a mixed number?
4. What is the meaning of negative signs in fractions?
5. How do you add or subtract mixed numbers?

Tip: Always ensure the denominators are the same before adding or subtracting fractions!