1. **State the problem:** Multiply the expressions $6pq^2$ and $2qr^2$. 2. **Recall the multiplication rule for algebraic expressions:** Multiply the coefficients (numbers) and then multiply the variables by adding their exponents if they have the same base. 3. **Multiply the coefficients:** $$6 \times 2 = 12$$ 4. **Multiply the variables:** - For $p$, it appears only in the first term, so it remains $p$. - For $q$, we have $q^2$ and $q^1$ (since $q$ is the same as $q^1$), so add exponents: $2 + 1 = 3$, giving $q^3$. - For $r$, it appears only in the second term as $r^2$. 5. **Combine all parts:** $$12 p q^3 r^2$$ 6. **Final answer:** $$12 p q^3 r^2$$