The box does not move because of friction acting in the opposite direction to the push, which balances the pushing force.
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Unbalanced forces cause an object to move in the direction of the greater force, thus bringing the object into motion or changing its state of motion.
When two opposite forces of different magnitudes pull the wooden block, the block begins to move in the direction of the greater force. These forces are unbalanced forces.
Balanced forces are forces that are equal in magnitude and opposite in direction, acting on an object such that they do not change the state of rest or motion of the object.
If equal forces are applied by pulling both strings X and Y simultaneously, the block will not move. These forces are balanced forces.