the situation is more complicated if you're just using nouns.

Essentially:

1. If you mix pronouns and nouns (or just use pronouns), all pieces in the compound possessive must be in possessive form:

Adam's and my apples
Amy's and my anniversary

2. If using only nouns and the possessed object(s) are shared, change only the last noun to its possessive form (in other words, if the object is shared, the apostrophe-s gets shared as well):

Amy and John's anniversary
John and Carol's cats (John and Carol jointly own the cats)

3. If using only nouns and the possessed objects are not shared, change each noun to its possessive form:

John's and Adam's backpacks (each has their own backpack)
John's and Carol's cats (each has their own cat or cats)


But the article points out that compound possessives usually sound pretty awkward, so it's probably better to just rephrase the sentence.