There are 6 moments, $6: 30, 6: 31, 6: 32, 6: 33, 6: 34, 6: 35$. At $\qquad$ moment, the hour hand and the minute hand are closest to each other, and at $\qquad$ moment, the hour hand and the minute hand are farthest from each other.
Analysis: Understand this as a pursuit problem on a circular track, where the minute hand moves 1 grid per minute, and the hour hand moves $\frac{1}{12}$ grid per minute. At 6:30, the interval between the hour hand and the minute hand is $30-30 \times\left(1-\frac{1}{12}\right)=2.5=\frac{30}{12}$ grids. The interval between the hour hand and the minute hand decreases by $\frac{11}{12}$ grids per minute. Therefore, at 6:31, the interval is $\frac{19}{12}$ grids, at 6:32, the interval is $\frac{8}{12}$ grids, at 6:33, the interval is $\frac{3}{12}$ grids, at 6:34, the interval is $\frac{14}{12}$ grids, and at 6:35, the interval is $\frac{25}{12}$ grids. Therefore, at 6:33, the hour hand and the minute hand are closest, and at 6:30, the hour hand and the minute hand are farthest.