#### Answer

$$-14q^{2}+11q-14$$

#### Work Step by Step

Initial equation: $-3(4q^{2}-3q+2)+2(-q^{2}+q-4)$
First, distribute the $-3$ to the first set of parenthesis, and the $2$ to the second:
$$-12q^{2}+9q-6-2q^{2}+2q-8$$ Then combine like terms to arrive at the final answer:
$$-14q^{2}+11q-14$$