A predicate tells us something about the subject. It includes a verb and any other modifiers. A compound predicate includes verbs that go with the same subject. Commas separate multiple predicates when there are three or more verb phrases, but a compound predicate with only two requires no punctuation to separate them.
Incorrect Deb walked to the store, but forgot her wallet.
Correct Deb walked to the store but forgot her wallet.
Incorrect Carleigh loves cooking, but hates washing dishes.
Correct Carleigh loves cooking but hates washing dishes.
Incorrect Tina called her mother, and invited her to lunch.
Correct Tina called her mother and invited her to lunch.