We can solve this by tracking the changes in temperature over each time interval:

1. At 9 AM, the temperature is given as $-2.1^\circ F$.

2. From 9 AM to 12 PM, the temperature increases by $10.8^\circ F$: $\text{Temperature at noon} = -2.1^\circ F + 10.8^\circ F = 8.7^\circ F$

3. From 12 PM to 3 PM, the temperature decreases by $13^\circ F$: $\text{Temperature at 3 PM} = 8.7^\circ F - 13^\circ F = -4.3^\circ F$

4. From 3 PM to 6 PM, the temperature drops by $18.4^\circ F$: $\text{Temperature at 6 PM} = -4.3^\circ F - 18.4^\circ F = -22.7^\circ F$

Thus, the temperature at 6 PM is $-22.7^\circ F$.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What would the temperature be at 3 AM if it continued dropping at the same rate?
2. What was the average temperature change between each recorded time?
3. If the temperature rose by 5°F after 6 PM, what would it be at 9 PM?
4. How much total temperature change occurred between 9 AM and 6 PM?
5. What would happen if the temperature fluctuated inversely between these intervals?

Tip: When solving word problems involving temperature changes, always track each time interval and keep an eye on whether the changes are increases or decreases.