To find the earliest time when all three meet back at the beginning, we need to find the least common multiple (LCM) of 4, 7, and 6.
Prime factorizing each number, we have $4=2^2$, $7=7$, and $6=2\cdot3$.
Taking the highest power of each prime that appears in any of the factorizations, we have $2^2\cdot3\cdot7=84$.
Therefore, the earliest time when all three meet back at the beginning is 84 minutes after 8:00, which is $\boxed{9:24}$.
The answer is: 9:24
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
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?

### Answer:
