1. **Problem:** Find the angle between the hour and minute hands at 20:12. 2. **Formula:** The angle between the hour and minute hands is given by $$\theta = \left|30H - 5.5M\right|$$ where $H$ is the hour and $M$ is the minutes. 3. **Apply values:** Here, $H=20$ and $M=12$. 4. Calculate: $$30 \times 20 = 600$$ $$5.5 \times 12 = 66$$ 5. Find the absolute difference: $$|600 - 66| = 534$$ 6. Since the maximum angle between clock hands is 180 degrees, subtract from 360 if angle > 180: $$360 - 534 = -174$$ Since negative, add 360: $$360 - 174 = 186$$ But 186 > 180, so take: $$360 - 186 = 174$$ 7. The smaller angle between the hands is $174$ degrees. **Final answer:** The angle between the hour and minute hands at 20:12 is $174$ degrees.