Final answer:
The gerund phrase 'repairing cars' functions as the object of the preposition 'by' in the sentence, indicating the method by which Brett earns his income.
Step-by-step explanation:
The gerund phrase in the sentence "Brett earns his income by repairing cars." is "repairing cars." The gerund phrase functions as the object of the preposition 'by,' which means it is the object of the preposition that shows Brett's method of earning income. The phrase itself includes the gerund 'repairing,' which is the -ing form of the verb used as a noun, and 'cars,' which is the object of the gerund.