At  what time between $6$ $a.m.$  and $7$ $a.m.$ will the minute hand and hour hand of a clock make an
angle closest to $60^0$?

1. $6:22$ $a.m.$
2. $6:27$ $a.m.$
3. $6:38$ $a.m.$
4. $6:45$ $a.m.$

edited