Recall that if $b$ and $d$ are nonzero, then  \[
\frac{a}{b}\cdot \frac{c}{d} = \frac{ac}{bd}.
\]In other words, to multiply fractions we just multiply numerators and multiply denominators. The product of the given numerators is $2\cdot 4=8,$ and the product of the given denominators is $3\cdot 7=21$. So the product of $\frac{2}{3}$ and $\frac{4}{7}$ is $\boxed{\frac{8}{21}}$.
Multiply $\frac{2}{3}$ by $\frac{4}{7}$.
{'answer': '\\frac{8}{21}', 'subject': 'Prealgebra', 'level': 1, 'unique_id': 'test/prealgebra/1776.json'}