You can use the right hand palm rule to determine the force acting on the speaker coil. Using the conventional current direction given, you can see that the current travels into the page as the wire goes up and out of the page when it goes down. The magnetic field exerts a force on the wire at these positions because the current in the wire travels perpendicular (or at some angle) to the magnetic field. Using the right hand palm rule at the top position where the wire goes into the page, point your thumb inwards (indicating conventional current direction inwards) and your fingers downwards in direction of magnetic field (N->S). Your palm shows that the force exerted on the wire is to the left. This causes the coil to move left and the speaker cone attached to the coil to move left.
note: You get the same direction of force for the current moving out of the page in the wire at the bottom but your thumb should point outwards and your fingers upwards instead.