The RG6 is designed for high frequency low level signals like satellite or antenna for TV distribution. So you would only normally be able to use this cable to connect up multiple cable/DVBT Receiver boxes/TV's.
Note that there is one other use for this cabling and that is to pass HDMI with a HDMI over Coax converter. This would allow you to have just the one Cable TV Box and pass its HDMI signal (along with other sources like roku/bluray/AppleTV etc into a modern AVR and then run HDMI out over coax converters to other rooms so they can share these central Video sources. Also note that with such a setup each room with a second TV would also get Audio signals along with the video which can be output over low quality TV speakers or via a connected sound device with speakers that is connected to TV's audio output port (this could be a soundbar or powered speakers or an amp/AVR with passive speakers).
Normally for mulitroom audio you would need to run proper speaker cables to speakers mounted in the room, walls or ceiling. And at the central cabling point in the basement you would have a small rack of multichannel amps and sources and control etc. Quite a lot of work to do all this and get all the cables pulled. If you have access to underfloor via basement and room spaces etc you may be able to do this cable pulling but it may be very hard to do it yourself with some house construction types...
I would actually recommend you don't go down this traditional route yourself and look at some of the more modern options instead. If you have Ethernet over cat5 and wifi to all rooms then you can get separate sound setups in each room and then join them up over the network. This setup requires no cable pulling or anything and is simply plug and play. The only issue is choosing the system that suits you. There are systems that are simple to use and very easy to control but you have to use all the same brand product so they work together. Sonos, Yamaha MusicCast and Denon Heos are examples of this and they each have their own advantages and limitations but they are not cheap. They often work best with speakers mounted in the room directly but you can connect them up to in-ceiling mounted speakers if you like the WallMart sound experience but the speaker wires have to go to the amplifier which can be located in the room or in any space you can find near by.
"So I have Gig ethernet in each room via Cat5E cable, so if its a straight ethernet setup do I have to change the plugs/wiring (no huge issue), the speakers I was planning to pull the baseboard and run speakers into the wall, now does that connect back to the Ethernet connection in each room and will a need an amp in every room? The Ethernet cables all go to a central switch in the basement next to the RG6 splitter for the TV.
The idea of one of the systems you mentioned is what I was looking for, a pad in each room to control the source/volume etc all leading back to a central amp/control system in the basement.
So one question I had do I lose the ethernet port or can I install a switch to keep it for occasional data usage? As my wife works from home and uses our bedroom as her office and plugs her laptop into get the Gig ethernet speed? We have AC wifi so Im not too heartbroken if you say no.
The other solution that is a bit more budget friendly is to use cheap ChromeCast Audios. With this setup each room just needs some powered speakers or an AVR/amplfier with separate speakers. And then you add a ChromeCast audio per device and you control the audio in one or more rooms from a phone/tablet. The only downside I see with this setup is that the power on/off control (and input selection on some audio devices) is not controlled from the casting application on your phone. You may need to walk up to your speakers/amp and push the power button etc or use their remote control to get them powered on and ready to output sound in that room. Some powered speakers may have auto signal detection power on/off control though. Also if sound quality is of high importance to you then ChromeCast audios may sound a bit better using their optical audio output into an AVR and decent speakers.
If you want to have video as well as audio to some rooms the setup would be a bit more complex.