An electric motor to various degrees depending on the field arrangements, function as a generator while running. This means that as they build up speed they tend to generate an internal voltage that opposes the applied voltage. The result is that the current falls and speed tends to settle without continual acceleration. The series connected field coil type motor as in starter motor have the greatest effect of reducing current with speed while the permanent magnet and shunt field coil have less effect.
Running any electrical load on 6 volts normally means that the power dissipated will be 1/4 of that when run on 12v.( half voltage and half current) However because of this internal generator effect the motor will draw more current so power available will be perhaps closer to half of that available on 12v.
If the motor has a commutator and brushes then give it a try. If it is like some tiny brushless DC fans the electronics may give trouble.
Now give us a hint what have you got in mind? olewill