A rocket is launched with constant acceleration, and four seconds after liftoff, a bolt detaches and falls to the ground, taking 6.40 seconds to reach the ground. To solve for the rocket's acceleration, one must first determine the bolt's velocity at the moment it falls, which is influenced by the rocket's acceleration during the initial four seconds. The bolt then accelerates downward under gravity ('g') for 6.40 seconds. The solution involves applying kinematic equations to relate the rocket's acceleration to the time and distance traveled by the bolt. The discussion emphasizes the importance of understanding the motion of both the rocket and the bolt to find the required acceleration.