To solve the expression \( \frac{2}{3}(-6 + 4) \), we first simplify the term inside the parentheses:
\[ -6 + 4 = -2 \]
Now substituting this back into the expression gives:
\[ \frac{2}{3}(-2) \]
Next, we can multiply \( \frac{2}{3} \) by \(-2\):
\[ \frac{2}{3} \times -2 = \frac{2 \times -2}{3} = \frac{-4}{3} \]
Thus, the value of the expression \( \frac{2}{3}(-6 + 4) \) is
\[ \boxed{-\frac{4}{3}} \]