The three 'volume control' wires coming into the living room are 4 conductors in a single jacket (red, black, green, white), right? Those go to the inputs of the volume controls. There should be wires that start at the volume control location and go to the actual speakers. If that is the case you'd just splice them together - red to red, black to black, green to red and white to black.
The three volume control wires then go to the outputs of the speaker selector.
In the tv room 6 speaker wires come in with 3 volume control wires
By this statement do you mean that in addition to the 3 volume control wires there are 6 other wires that come out from the wall in the living room? If so they could be entirely unrelated to the volume controls or they could be coming straight from the speakers and are not currently hooked up to the volume control at all.