Facetime can't be reached

I am unable to connect with Facetime on my Monterey system, but the reverse works fine. That is, from my Sonnoma system, it won'd connect to my Monterey system, but from my Monterey system, I can connect with my Sonoma system. In Facetime Preferences, on the Monterey system, "You can be reached for Facetime at" is dimmed (though with my right e-mail and box checked). I have to assume this is telling me that I can't be reached by Facetime on that Monterey system. How do I fix this??? I am logged into my iCloud on that system, so it isn't matter of my Mac not knowing who I am.