[Fyron]

The total net force on the block is 0. The force of gravity is balanced by the "normal force" that the ground applies back to the block (equal magnitude but exactly opposing direction). The force that person A exerts on the block is exactly the same in magnitude as the force that person B exerts on the block, but in the opposite direction. Note that Force = Mass X Acceleration. If there is no net force, there is no acceleration, thus no change in velocity. Since the initial velocity of the block was 0, it remains 0.