1. **State the problem:** We need to find the temperature at the mountain top given that the village temperature is 3°C and the mountain top temperature is 12°C lower. 2. **Formula and explanation:** To find a temperature that is lower by a certain amount, we subtract that amount from the original temperature. 3. **Set up the equation:** Let $T_m$ be the temperature at the mountain top. $$T_m = 3 - 12$$ 4. **Calculate:** $$T_m = \cancel{3} - 12 = -9$$ 5. **Answer:** The temperature at the mountain top is $-9^\circ C$.