Let's break this down step by step.

We have the expression:

$\left(\frac{-2}{3}\right)^2 - \frac{3}{4} \times \left(2 \frac{1}{3}\right)$

Step 1: Solve the first part $\left(\frac{-2}{3}\right)^2$

$\left(\frac{-2}{3}\right)^2 = \frac{(-2)^2}{3^2} = \frac{4}{9}$

Step 2: Convert the mixed number $2 \frac{1}{3}$ to an improper fraction

$2 \frac{1}{3} = \frac{7}{3}$

Step 3: Multiply $\frac{3}{4}$ by $\frac{7}{3}$

$\frac{3}{4} \times \frac{7}{3} = \frac{21}{12} = \frac{7}{4}$

Step 4: Combine the results

Now we have the expression: $\frac{4}{9} - \frac{7}{4}$

Step 5: Find a common denominator

The least common denominator (LCD) between 9 and 4 is 36. We convert the fractions:

$\frac{4}{9} = \frac{16}{36}$ $\frac{7}{4} = \frac{63}{36}$

Step 6: Perform the subtraction

$\frac{16}{36} - \frac{63}{36} = \frac{16 - 63}{36} = \frac{-47}{36}$

Thus, the final result is: $\frac{-47}{36}$

Would you like more details or have any questions?

Here are some related questions:

1. How do you convert between improper fractions and mixed numbers?
2. What are the steps for finding a common denominator?
3. How do negative exponents affect fractions?
4. How do you simplify complex fractions?
5. Why is multiplying fractions easier than adding them?

Tip: When subtracting fractions, always remember to find the least common denominator to ensure accuracy.