1. The problem is to simplify the expression $\frac{\sqrt{12} \cdot \sqrt{2}}{\sqrt{24}}$ and compare it to the given options. 2. Recall the property of square roots: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$. 3. Apply this property to the numerator: $$\sqrt{12} \cdot \sqrt{2} = \sqrt{12 \times 2} = \sqrt{24}$$ 4. Substitute back into the expression: $$\frac{\sqrt{24}}{\sqrt{24}}$$ 5. Since any nonzero number divided by itself is 1, we have: $$1$$ 6. Therefore, the simplified value of the expression is 1. 7. Now, check the options: - $\sqrt{24}$ is not equal to 1. - $4\sqrt{6}$ is not equal to 1. - $6\sqrt{6}$ is not equal to 1. - $2\sqrt{6}$ is not equal to 1. None of the options equal 1, so none of the buttons represent the simplified expression exactly. Final answer: The expression simplifies to 1, which is not listed among the options.