Final answer:
The ball thrown directly upward with an initial speed of 12.0 m/s will return to the hand at the same speed of 12.0 m/s, assuming no energy is lost to external forces.
Step-by-step explanation:
When a ball is thrown directly upward and it leaves your hand with a speed of 12.0 m/s, neglecting air resistance, it will return to your hand at the same speed but in the opposite direction. According to the principles of conservation of energy and assuming no energy is lost to air resistance or other forces, the kinetic energy of the ball when thrown upwards will eventually be converted into potential energy at the peak of the ball's trajectory. As the ball falls back to your hand, this potential energy is converted back into kinetic energy. Therefore, disregarding any external forces, the ball will be traveling at 12.0 m/s when it returns to your hand.