If I understand you correctly:
1. You ran speaker wire to your speakers, and they are hooked up fine.
2. You ran RG-6 to your display for output from your video devices - and this is fine.
3. You ran speaker wire to your line level inputs on the TV and are now wondering how to put RCA ends on them. This is an issue.
I'm a bit confused as to whether you are using a surround receiver. This is typically the case and your VCR, DVD, etc., would be located about 12 inches from your receiver and while video may run straight to the TV, audio would just use one foot interconnects (often digital) to connect to the receiver.
If the audio you are trying to connect is an unamplified signal, coming out of the red and white RCA jacks on the back of your (for example) VCR. Then, you are correct in thinking that 12 gauge cabling was not the correct type to run.
If it is next to impossible to put a coax cable in place, then you will definitely want to try to solder RCA connectors onto the 12 gauge cable, and hope you have enough wires run. You also need to pray that there is no noise in your home that will mess up your audio signal. Speaker cable is designed to carry a high powered signal. That power helps to keep noise off the line and out of the speakers. With line level audio, which is what you want to connect, there is hardly any power there and any interference or noise can be relatively easily transferred to the speaker cables.
Unless they are shielded - which they probably aren't.
Yuck, not what you want to hear and I'd love to say 'No problem, just do...' and have your problem fixed. Pick up a couple of inexpensive RCA solder on ends, and spend a bit of time soldering. You can run line level audio over the cables with no problem. But, the quality of the final sound may be compromised. Significantly. Be ready for that potential.