To find the quotient of \(\frac{8}{3}\) divided by \(\frac{2}{3}\), we can rewrite the division of fractions as multiplication by the reciprocal:
\[ \frac{8}{3} \div \frac{2}{3} = \frac{8}{3} \times \frac{3}{2} \]
Now, multiply the fractions:
\[ \frac{8 \times 3}{3 \times 2} = \frac{24}{6} \]
Next, simplify \(\frac{24}{6}\):
\[ \frac{24}{6} = 4 \]
Thus, the quotient in simplest form is \(4\).
So the answer is:
\[ \boxed{4} \]
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