The minute hand moves 360 degrees in 60 minutes, or 6 degrees per minute. The hour hand moves 360 degrees in 12 hours, or 0.5 degrees per minute. At 6:00 PM, the hour hand is at 180 degrees and the minute hand is at 0 degrees. The relative speed of the minute hand with respect to the hour hand is 5.5 degrees per minute. For the minute hand to be 3 minutes ahead, it needs to be 3 * 6 = 18 degrees ahead of the hour hand. The time taken for the minute hand to gain 18 degrees on the hour hand after 6:00 PM is 18 / 5.5 minutes, which is approximately 3.27 minutes. However, the question asks for the minute hand to be 3 minutes *ahead* of the hour hand, which implies a specific angular separation. We can also solve this by calculating the position of hands at each option. At 6:36 PM, the minute hand is at 36 * 6 = 216 degrees. The hour hand is at (6 + 36/60) * 30 = (6.6) * 30 = 198 degrees. The difference is 216 - 198 = 18 degrees, which is equivalent to 18/6 = 3 minutes.