Answer
$16y^2z^3-\frac{8}{35}yz^4.$
Work Step by Step
By multiplying each term of the polynomial by the factor $\frac{4}{7} y z^{3}$, and then adding the products, we have
$$
\frac{4}{7} y z^{3}\left(28 y-\frac{2}{5} z\right)=\frac{4}{7} y z^{3}\left(28 y\right)+\frac{4}{7} y z^{3}\left(-\frac{2}{5} z\right)\\
=16y^2z^3-\frac{8}{35}yz^4.
$$
