To solve the expression $\sqrt{18} \times \sqrt{32}$, we can simplify each square root first. Step 1: Simplify $\sqrt{18}$. We find the largest perfect square factor of 18. $18 = 9 \times 2$ So, $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$. Step 2: Simplify $\sqrt{32}$. We find the largest perfect square factor of 32. $32 = 16 \times 2$ So, $\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$. Step 3: Multiply the simplified square roots. $$ \sqrt{18} \times \sqrt{32} = (3\sqrt{2}) \times (4\sqrt{2}) $$ Multiply the coefficients and the square roots separately: $$ = (3 \times 4) \times (\sqrt{2} \times \sqrt{2}) \\ = 12 \times (\sqrt{2})^2 \\ = 12 \times 2 \\ = 24 $$ Alternatively, we can multiply the numbers inside the square root first: $$ \sqrt{18} \times \sqrt{32} = \sqrt{18 \times 32} \\ = \sqrt{576} $$ Now, find the square root of 576. $$ \sqrt{576} = 24 $$ The final answer is $\boxed{24}$.