To solve the expression \( \frac{2}{3} - \frac{1}{9} + \frac{2}{9} \), we need to perform the operations step by step.

First, let's find a common denominator for all the fractions. The denominators are 3 and 9. The least common denominator (LCD) is 9.

Convert \(\frac{2}{3}\) to a fraction with a denominator of 9:
\[
\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}
\]

Now the expression is:
\[
\frac{6}{9} - \frac{1}{9} + \frac{2}{9}
\]

Since all the fractions now have the same denominator, we can combine them by adding and subtracting the numerators:
\[
\frac{6 - 1 + 2}{9} = \frac{7}{9}
\]

So, the value of the expression \( \frac{2}{3} - \frac{1}{9} + \frac{2}{9} \) is:
\[
\frac{7}{9}
\]