1. The problem asks which two terms should be switched to arrange the list in ascending order. 2. The list given is: $$\left| -\frac{12}{5} \right|, -\frac{1}{\frac{3}{4}}, 0.5, -4$$. 3. First, simplify each term: - $$\left| -\frac{12}{5} \right| = \frac{12}{5} = 2.4$$ - $$-\frac{1}{\frac{3}{4}} = -\frac{1}{0.75} = -\frac{4}{3} \approx -1.333$$ - $$0.5$$ is already simplified. - $$-4$$ is already simplified. 4. So the list is: $$2.4, -1.333, 0.5, -4$$. 5. To arrange in ascending order, the numbers should be from smallest to largest: $$-4, -1.333, 0.5, 2.4$$. 6. The original list order is: $$2.4, -1.333, 0.5, -4$$. 7. To get the ascending order, switch $$2.4$$ and $$-4$$. 8. Therefore, the two terms to switch are $$\left| -\frac{12}{5} \right|$$ and $$-4$$. Final answer: Switch $$\left| -\frac{12}{5} \right|$$ and $$-4$$ to arrange the list in ascending order.