I have a new Sonos Amp with existing speakers at my home. Each room has 2 speakers and they use a 4 conductor wire (black, white, red, and green). Should I only use the red and black wire to connect to the amp? Can I connect all the speakers to one amp?
Living Room: 2 speakers, 2 cables
Kitchen: 2 speakers, 1 cable
Basement: 2 speakers, 1 cable
Back Yard: 2 speakers, 1 cable
Hey
Welcome to the Sonos Community, thank you for your post and apologies for the late response.
I’m not familiar with the wiring you have but had a look around here. I hope the matter of how to connect the different cables becomes clear with this: 4 wire speaker connection | Sonos Community
Regarding hooking up all speakers to the one Sonos Amp - You can connect up to 4 speaker to an Amp depending on the impedance rating of your speakers, but in that case you also need to consider that the connections on the Amp are split between left and right stereo. Not an ideal sound situation when you only have the right channel in the basement and the left only in the kitchen - standing on the stairs for the optimal listening experience 
If you want to have the full sound in each room and also control each room separately you need an Amp for each room.
Hope this helps!
I would also add to this the mono setting for the amp that would sum the stereo signal into dual mono, so each room would get the same audio output.
In this situation though, I would spring for at least a second amp.
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