We have 6 home pods in our house. They are all synced up. Two are in our Living Room and every time our daughter uses the Intercom feature to tell us something the two in the Living Room produce an echo and we can

Hi k6mk6,

We'll be glad to assist further. We assume by synced, you mean they're set up in a stereo pair. If so, you shouldn't notice an echo or similar on each device. With that said, we'd recommend restarting each HomePod then seeing if the issue persists after the restart.

Steps for doing so can be found in If HomePod or HomePod mini isn't responding - Apple Support

"Restart HomePod or HomePod mini

1. Open the Home app on your iPhone, iPad, or Mac that's signed in with the Apple ID that you used to set up HomePod.
2. Tap or click HomePod.
3. Scroll down, or tap or click the Settings icon  and scroll down.
4. If you have two HomePod speakers set up as a stereo pair, select Restart HomePod. If your HomePod speaker is not set up as a stereo pair, select Reset HomePod, then select Restart HomePod. 

If you don't see an option to restart your HomePod, unplug it from power, then plug it back in and try again.

If HomePod still doesn't respond, reset it."

If it does, you may want to reach out to Apple to look into this with you further: Get Support

Cheers.