Suppose box A is connected to a larger box B, and both are on top of a frictionless surface. My hand applies a force to box A in the direction of box B (Fha), causing boxes A and B to move. So box B moves. By Newton's third law, the force exerted by box B on to box A (Fba) = -the force exerted by box A on to box B (Fab). Now, the only force (that we care about for now) external to the system is Fha, then Fha = Fab = -Fba. So mathematically, Box A should not move.

Technically, though, we can apply a force such that Box A and Box B both move. So the net force acting on box A > Fba. How is this possible?

Suppose box A is connected to a larger box B, and both are on top of a frictionless surface. My hand applies a force to box A in the direction of box B ($F_{ha}$), causing boxes A and B to move. So box B moves. By Newton's third law, the force exerted by box B on to box A ($F_{ba}$) = -the force exerted by box A on to box B ($F_{ab}$). Now, the only force (that we care about for now) external to the system is $F_{ha}$, then $F_{ha} = F_{ab} = -F_{ba}$. So mathematically, Box A should not move.

Technically, though, we can apply a force such that Box A and Box B both move. So the net force acting on box A > $F_{ba}$. How is this possible?