Consider case 1:- When only magnet move right the no of field line crossing through the coil is increases, i.e, Lenz's law current
i induced so that minimize or oppose the increment of the field line. Therefore current induced anty clockwise and hence galvanometer deflect right.
Case-2:- Magnet and coil both moving right.R relative motion between magnet and coil is zero i.e, no of field crossing through coil doesn't change. Hence no current induced in the coil galvanometer shows no deflection.