1. **State the problem:** Multiply the expressions $3x^2$ and $6xy$. 2. **Recall the multiplication rule for algebraic terms:** When multiplying terms with the same base, add their exponents. For example, $x^a \times x^b = x^{a+b}$. 3. **Multiply the coefficients:** $3 \times 6 = 18$. 4. **Multiply the variables:** - For $x$: $x^2 \times x^1 = x^{2+1} = x^3$. - For $y$: $y$ appears only in the second term, so it remains $y^1$. 5. **Combine the results:** $$18x^3y$$ **Final answer:** $18x^3y$