Correct Answer - Option 2 : 15°
The hour needle travels 30° while the minute needle travels 360°.
Implies, when the minute needle will travel 180° the hour needle will travel 15°.
Thus, when the minute needle will reach at 6, the hour needle would be exactly between 6 and 7.
Hence, the difference between them would be 15°.
Alternate Method:
At 6'o clock, the hour hand will be at 180° from the hour hand. Now 30 minutes past 6 meaning 6:30.
In 30 minutes the hour hand will travel 1/2 × 30° = 15°
The final position of hour hand will be = 180° + 15° = 195°
Whereas the final position of the minute hand will be 180°
So angle between them = 195° - 180° = 15°
Hence, the answer is 15°.