One way to do this is to find the least common multiple (LCM) of 4, 7, and 6. To find the LCM, I can use the prime factorization of each number and take the highest power of each prime that appears. 4 = 2^2, 7 = 7^1, and 6 = 2^1 * 3^1. The highest power of 2 is 2^2, the highest power to 7 is 7^1, and the highest power of 3 is 3^1. So the LCM is 2^2 * 7^1 * 3^1 = 4 * 7 * 3 = 84. This means the earliest time they all meet back at the start is 84 minutes after 8:00, which is 9:24. 
Anna, Stephanie, and James all start running around a track at 8:00. Anna completes a lap every 4 minutes, Stephanie finishes a lap every 7 minutes, and James finishes a lap every 6 minutes. What is the earliest time when all three meet back at the beginning?