Avg Speed is Distance/Time. You need to find the total distance traveled and the total time.
From the first part, you know Jack ran for 1 hour, and Jack ran 4 miles. 4 miles/hour * 1 hour = 4 miles.
The second part tells you how far Jack cycled. It's 6 hours. To find the time it took, use Distance = rate x time to find the time. Time = Distance/Rate = 6/12 = 1/2 hour.
Jack's total distance traveled is 4 + 6 = 10 miles. The total time is 1 + 1/2 hour = 3/2 hour.
The average speed is 10/(3/2) = 10 * 2/3 = 20/3 miles per hour = approximately 6.67 miles per hour.