If a wire of length L carrying a current I lies in a magnetic field B, the force on the wire due to the interaction between magnetic fields is given by F = `I*LxxB` .
In the problem, the wire of length 55.5 cm carrying a current of 8.75 A lies in a uniform magnetic magnetic field. The wire experiences a maximum force of 1.28 N towards the south when the current flows toward the east. Here the direction of the current in the wire and the force acting on it are perpendicular to each other.
If the magnitude of the magnetic field is B,
1.28 = 8.75*0.555*B
=> B `~~` 0.26357 T
If the force and current are represented on a sheet of paper and point towards the south and east respectively, the magnetic field is perpendicular to the two and points in a direction out of the sheet.