To solve this expression, we first square the fraction -2/3:

(-2/3)² = (-2/3) * (-2/3) = 4/9

Then, we add 4/3 to the result:

4/9 + 4/3

To add these fractions, we need to find a common denominator. The least common multiple of 9 and 3 is 9. So, we can rewrite the fractions with the common denominator of 9:

4/9 + 4/3 = (4/9) + (4/3) * (3/3) = 4/9 + 12/9

Now that the fractions have the same denominator, we can add them:

4/9 + 12/9 = (4 + 12)/9 = 16/9

Therefore, the expression (-2/3)² + 4/3 equals 16/9.