Kind of a necro here, but simple power tutorial:
A (Amperage) * V (Voltage) = W (Wattage).
What you asked for your device you want to power was 12v at 9Ah (Amp-hours), 12*9 = 108. That means every hour, your device will use 108W - in another notation, your device uses 108Wh (Watt-hours).
If you want to power that 108Wh with 6v, you'll have to use algebra and rearrange the first equation I gave you:
A*V=W, if you want V alone, A=W/V. That means if you take your wattage, 108, divide it by the voltage you want to power it from, 6, you get 108/6 = 18. That means if you wanted to power it from 6v, you'd need 18Ah instead of just 9. That's not account for power lost during the 'boosting' from 6v to 12v, which would mean you'd probably need something more like 20Ah.
Long story short: This is going to be expensive no matter how you come at it, pretty much. Good luck.