We use the right hand rule when we want to find the direction of magnetic feild of a straight current carrying conductor.
It goes like this: point u r thumb in the direction of the current, then direction of the magnetic feild is the direction which u r curled fingers point.
Flemings left hand thumb rule gives u the direction in which the coil in a motor moves.
Here the thumb, index and middlefinger's r held mutually perpendicular to each other. Then the forefinger points direction of current, the middlefinger shows direction of magnetic feild, then the thumb shows direction of motion of the coil.