Let's solve the expression step by step:

$- \frac{5}{6} + \left(2 - \frac{2}{3}\right)$

1. First, solve the expression inside the parentheses: $2 - \frac{2}{3}$ To subtract, convert 2 to a fraction with the same denominator as $\frac{2}{3}$: $2 = \frac{6}{3}$ So, $\frac{6}{3} - \frac{2}{3} = \frac{4}{3}$

2. Now, the expression becomes: $-\frac{5}{6} + \frac{4}{3}$

3. To add these fractions, find a common denominator. The common denominator between 6 and 3 is 6: $\frac{4}{3} = \frac{8}{6}$ So the expression becomes: $-\frac{5}{6} + \frac{8}{6}$

4. Now, subtract the numerators: $\frac{-5 + 8}{6} = \frac{3}{6} = \frac{1}{2}$

So, the final answer is $\frac{1}{2}$.

Would you like more details or have any questions?

Here are some related questions:

1. How do you find a common denominator between two fractions?
2. What are the steps to simplify a fraction?
3. How can you convert a mixed number to an improper fraction?
4. What is the difference between adding and subtracting fractions?
5. How do you handle negative numbers in fraction operations?

Tip: Always simplify fractions at the end of your calculations to make your answer as clear as possible.