What kind of power supply can power this stepper motor connected to an Arduino?
If you wanted to use the battery, the positive terminal of the battery would connect to the "V2" pin of the L93D and the negative terminal would be connected to your common ground.  The "1in" and "4inn" pin would be connected to your Arduino I/Os.

You could also use a DC-DC boost converter taking the 5V input and outputting 12V.