Final answer:
The appositive phrase in the sentence is 'a former Olympic champion', providing additional information about 'The gym teacher'.
Step-by-step explanation:
The words that constitute the appositive phrase in the sentence "The gym teacher, a former Olympic champion, complimented Patty Bouvier on her cartwheels." are "a former Olympic champion." This phrase adds explanatory information to the noun "The gym teacher," telling us more about who the teacher is. An appositive can provide additional details or clarifications about a noun and is usually set off by commas, dashes, or parentheses depending on its importance in the sentence and the emphasis the writer wants to convey.