I wouldn't power the RC receiver from a different voltage from the voltage it is designed for. But you can use a regulator from your 12V supply to drop the voltage down to 6V for the RC receiver.
The H-bridge motor driver is explained pretty nicely at
http://www.botskool.com/tutorials/electronics/general-electronics/motor-controller-h-bridge
Read down to Fig. 3 but not the stuff about the L293 IC.
Now you should understand how an H-bridge drives a motor and can make it run in either direction.
Each half of the H-bridge produces an output voltage that is either high (positive voltage) or low (zero volts). The motor will turn if it sees a voltage difference between one side and the other; in other words, if the two halves of the H-bridge are outputting different states. If the two sides are outputting the same state (either both high or both low), the motor will not see any voltage across it, so it won't turn.
For your application, you need to boost those voltages, so instead of each side of the H-bridge producing 0V or 6V, it produces 0V or 12V.
An SPDT (single-pole double-throw) relay, also called SPCO (single-pole changeover), has a coil that is energised by voltage, and a set of contacts with three connections. See
http://www.learningaboutelectronics...a-single-pole-double-throw-relay-in-a-circuit for a good simple explanation.
If you connect a relay coil between the output of one side of the H-bridge and the 0V rail, the relay will follow that side of the H-bridge. When that H-bridge output is low, the relay will see no voltage, and its COM terminal will be connected to its NC terminal. When that H-bridge output is high, the relay will see voltage across its coil, so it will energise, and its COM terminal will be connected to its NO terminal.
So you need to connect the contact to the power supply like this:
NO terminal: to +12V
NC terminal: to 0V (negative side of the 12V power supply)
COM terminal: to one side of the motor.
Then you use a second relay, connected to the other side of the H-bridge, to drive the other side of the motor. Voila! You have a buffer that can drive the motor in either direction, from a higher voltage, and is controlled by the existing outputs from the H-bridge.
Your relays must have 6V coils, because they're being driven from the H-bridge, which is powered from 6V. Their contacts must be rated for at least 8A. You should also have some kind of snubbing to protect the contacts from the back EMF from the motor. Do you understand how the relays will work?