The question is about time, speed, and distance on a circular track. `A` walks one round per hour and `B` runs six rounds per hour, which means `B` is five times faster than `A`. They start together, so they will meet when `B` completes one more round than `A`. If `A` completes one round in an hour, `B` completes this in 1/5th of an hour which is 12 minutes (60/5).
Option 1 and 2 are both over an hour after they start, this wouldn`t be the first time they cross. `B` should be catching up to `A` before an hour. Option 3, 7:48 a.m., is 18 minutes past start time, while option 4, 7:42 a.m., is 12 minutes past 7:30 a.m. which matches with the calculation above. Therefore, option 4 is correct. They will cross each other first at 7:42 a.m.