There is one outlet box with wiring included. Wires are Red, Black, White, & Green. I know about red and black but wasn't sure about white and green. We also need to purchase a receiver but wanted to make sure we purchase one that will work - does it need to be at least a 4 channel receiver? Excuse my negligence with this, I do have no experience. Thanks in advance!
There is no real way to know what the wiring goes to without tracing it back to the speakers if nothing is labeled. There is no set rule as to what colors mean what, while red and white is usually left/right speaker that does not mean that your setup is done that way. Yes you want a multi zone amplifier for those speakers.
If you have 4 speakers, you should have 4 pairs or wires.
Is there a single speaker in each room?
If so remove it and check if the speaker has 2 or 4 terminals. There are single stereo speakers that will have 4 terminals each.
Since you only have four wires coming from the wall there is no way that each speaker has wiring going back to the central location.
You can determine how the speakers are connected by using a AA battery. Connect the negative terminal of the battery to one speaker wire and tap the plus terminal with one of the other wires. The speaker or speakers will make a click as the woofer moves in or out. Try different combinations of the 4 wires. When they are in phase the woofer moves out. That means that the wire connected to the plus battery terminal is a plus connection to the speaker.
Definitely not a proper set up. Each speaker should have at least two wires home run back to the central location. You won't be able to play or adjust the volume of each room individually.
You don't need a 4 channel receiver. You will likely need a stereo receiver with speaker A + B terminals. One with mono button would be good since each room would only be able to play left or right channels but not both.
A Sonos AMP or Denon HeosAmp can play 4 speakers at the same time. Might be a better choice than a receiver.