To solve $-\frac{5}{6} + \frac{2}{3}$, we need to make sure both fractions have the same denominator.

The least common denominator (LCD) of 6 and 3 is 6, so we rewrite $\frac{2}{3}$ with 6 as the denominator: $\frac{2}{3} = \frac{4}{6}$

Now, the equation becomes: $-\frac{5}{6} + \frac{4}{6}$

Since the denominators are the same, we can subtract the numerators: $-\frac{5}{6} + \frac{4}{6} = \frac{-5 + 4}{6} = \frac{-1}{6}$

So, the result is: $-\frac{1}{6}$

Would you like more details on any part of this? Here are 5 related questions:

1. How do you find the least common denominator between two fractions?
2. What are the rules for adding and subtracting fractions with different denominators?
3. How do negative signs affect fractions in addition or subtraction?
4. Can you show an example of adding fractions with unlike denominators?
5. How do you simplify fractions?

Tip: When adding or subtracting fractions, always find a common denominator before performing the operation.