In this question, we are dealing with a mass-spring system. When a mass m is hung on a spring, it causes the spring to stretch. The amount of stretch in the spring can be used to determine the value of the spring constant, k. In this case, the spring is stretched by 6 cm.

Now, when the loaded spring is pulled downward a little and released, it starts to oscillate. The period of vibration, T, is the time taken for one complete cycle of oscillation.

The period of vibration of a mass-spring system is given by the formula T = 2π√(m/k), where m is the mass and k is the spring constant. Since the mass does not change in this question, we only need to consider the spring constant.

As the spring is stretched by 6 cm, we can conclude that the spring constant is not changed in this scenario. Therefore, the period of vibration will remain the same.

Looking at the provided options, we can see that option 4, 0.64 s, is the correct answer, as it matches our understanding that the period of vibration remains unchanged when the loaded spring is pulled downward and released.