Does he currently have volume controls in all the rooms?
Are there currently speakers in all of the rooms?
If there are volume controls in place, you will want to find out if they are impedence matching, they may be.
A single amp and a speaker selector (not an A/V receiver) is generally a very solid solution for not a lot of cash.
There are also multi-channel amps out there for about $500 for 12 channels (6 speaker pairs). This works really well for multiple rooms/zones which have volume controls in place already.
An A/V receiver may work, but it won't provide a lot of power across 6 speaker pairs, and is more likely to have long term issues as it will be running a heavy load most of the time. But, it can offer multiple source selection and perhaps built in remote smartphone access which may be nice.
Still, I would hope there are volume controls in the rooms and I would just add something like this:
SpeakerCraft BB1235 12X35W Amplifier 664254000348 | eBay
Gives you discrete amplification across a full 6 pairs of speakers. But, you will need volume controls or some sort of preamp to help ensure things work properly.