To solve when the minute hand is 3 minutes ahead of the hour hand:

At 6:00, the hour hand is at $180^{\circ}$.

The minute hand moves $6^{\circ}$ per minute, and the hour hand moves $0.5^{\circ}$ per minute.

The difference between them should be $18^{\circ}$ (since 3 minutes = $18^{\circ}$).

Equation: $6t = 180 + 0.5t + 18$

Simplify: $5.5t = 198$ $t = 36$

So, at 6:36 PM, the minute hand is 3 minutes ahead of the hour hand.

Answer: C. 6:36 PM