We can calculate the temperature at each time step by adding or subtracting the changes.

1. Initial temperature at 9 am: $-6.7^\circ F$

2. Between 9 am and noon:
   The temperature rose by $10.7^\circ F$.
   New temperature:
   $-6.7^\circ F + 10.7^\circ F = 4.0^\circ F$

3. Between noon and 3 pm:
   The temperature rose by $14.8^\circ F$.
   New temperature:
   $4.0^\circ F + 14.8^\circ F = 18.8^\circ F$

4. Between 3 pm and 6 pm:
   The temperature decreased by $12.9^\circ F$.
   New temperature:
   $18.8^\circ F - 12.9^\circ F = 5.9^\circ F$

Thus, the temperature at 6 pm was $5.9^\circ F$.

Would you like further details or have any other questions?

Here are five related questions:

1. What would be the temperature at 9 pm if it decreased by 5°F after 6 pm?
2. How would you calculate the average temperature change per hour during the day?
3. If the temperature increased by 7.5°F every hour after 6 pm, what would it be at midnight?
4. What if the initial temperature at 9 am was $0^\circ F$? How would the result change?
5. Can you create a temperature graph showing the changes during the day?

Tip: Always double-check units (e.g., °F or °C) to avoid calculation errors in temperature problems!