To find the quotient of \( \frac{9}{10} \) and \( \frac{2}{3} \), we can divide \( \frac{9}{10} \) by \( \frac{2}{3} \). Dividing by a fraction is the same as multiplying by its reciprocal.
So, we can rewrite the expression:
\[ \frac{9}{10} \div \frac{2}{3} = \frac{9}{10} \times \frac{3}{2} \]
Now, we can multiply the fractions:
\[ \frac{9 \times 3}{10 \times 2} = \frac{27}{20} \]
Thus, the quotient of \( \frac{9}{10} \) and \( \frac{2}{3} \) is \( \frac{27}{20} \).
So, the answer is \( \frac{27}{20} \).