To find the quotient of \( \frac{2}{3} \) (two-thirds) and \( \frac{2}{9} \) (two-ninths), we can divide the two fractions:
\[ \text{Quotient} = \frac{2/3}{2/9} \]
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ \frac{2/3}{2/9} = \frac{2}{3} \times \frac{9}{2} \]
Now we multiply the fractions:
\[ = \frac{2 \times 9}{3 \times 2} = \frac{18}{6} = 3 \]
Therefore, the quotient of two-thirds and two-ninths is:
\[ \boxed{3} \]
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