#### Answer

$$z^{4}-9z^{3}+12z^{2}+8z$$

#### Work Step by Step

Initial Equation: $-z^{3}(9-z)+4z(2+3z)$
Distribute the $-z^{3}$ and $4z$ to their respective sets of parenthesis:
$$-9z^{3}+z^{4}+8z+12z^{2}$$ Then combine like terms to simplify to get final answer:
$$z^{4}-9z^{3}+12z^{2}+8z$$ (There are no like terms in this problem so simply rearrange in order from highest exponent to lowest)