How would I connect several speakers to an amplifier for multi room sound?
You start by having all wires run directly to where the amplifier is. If each room is going to have an impedence-matching volume control knob then you run your speakers to that knob and then from that to the amp.

Do not chain or parallel wire you speakers in wall. Even though 8 Ohm speakers might be ok in parallel for your 4 Ohm amplifier you should make that circuitry outside of the wall at the amp location.

You can't just combine left and right outputs and form mono sound. You'll need a device which can mix the stereo inputs into a mono output. If you want to do this it is likely you will need to have pre-outs on your receiver, and a second amplifier stage for rooms C and D.

My suggestion would be not to bother with mono in rooms C and D. Buy single-location speakers that have dipole coils in them so that you can run stereo sound (four conductors) to the one speaker.

In this configuration, you have four stereo requirements.

I suggest you get a switching splitter designed for this, or a power amp stage designed to power eight channels.