Find the product.
\[
\frac{2}{7}\left(-4 \frac{2}{3}\right)
\]
\[
\frac{2}{7}\left(-4 \frac{2}{3}\right)=
\]
(Type an integer or a simplified fraction.)

Step 1 ：Convert the mixed number (-4 2/3) to an improper fraction. The formula for converting a mixed number to an improper fraction is \(\text{{whole number}} \times \text{{denominator}} + \text{{numerator}}\). So, \(-4 \times 3 + 2 = -10\). Therefore, -4 2/3 as an improper fraction is -10/3.

Step 2 ：Next, multiply the two fractions together. The formula for multiplying fractions is \(\frac{{\text{{numerator1}} \times \text{{numerator2}}}}{{\text{{denominator1}} \times \text{{denominator2}}}}\). So, \(\frac{2}{7} \times \frac{-10}{3} = \frac{-20}{21}\).

Step 3 ：Finally, simplify the fraction if necessary. In this case, the fraction \(-20/21\) is already in its simplest form.

Step 4 ：Final Answer: The product of the two fractions is \(\boxed{-\frac{20}{21}}\).