Hold thumb, forefinger and middle finger mutually perpendicular: forefinger = field, middle finger = current, thumb = force/motion. The left hand gives the motor force direction; the right hand gives the generator's induced current direction.
Three mutually perpendicular directions — assign them with the correct hand for motor vs generator.
F = B × I × L × sin θ
F
force on the conductor (newtons)
B
magnetic field (teslas)
I
current in the conductor (amperes)
L
length of conductor in the field (metres)
θ
angle between conductor and field
In plain English: Same three fingers, two jobs: left hand when current causes motion (motor), right hand when motion causes current (generator). Remember the left-hand fingers as F-B-I from thumb inward: Force, field (B), current (I).
Where you'll meet it: Every 'which way does it spin / which way does current flow' question — motors, generators, loudspeakers, and the direction check when wiring a DC motor at the bench.