Using the right-hand rule for forces, which way does this rod rotate?
The rod or metal core will rotate anticlockwise.
The positive end of the battery is shown by the longer "line". Current flows rightwards at the battery and downwards at the rightmost straight wire.
Looking at how the wires are coiled around the core, the visible wires have current running at an angle downwards (more down than up).
Using the right hand grip rule, your thumb should be pointed at the end nearer to the N-pole of the large magnet. Thus, the magnetic field generated in the core goes from "left to right" (at an angle), inducing a N-pole nearer to the N-pole of the large magnet.
Therefore, the N-poles will repel and the core will spin anticlockwise.