Final answer:
The entire gerund phrase in Brett earns his income by repairing cars is 'repairing cars' and it functions as the object of the preposition 'by'. The correct answer is option a.
Step-by-step explanation:
The correct answer to the question is 'a. repairing cars'; it is the entire gerund phrase in the sentence, and its noun function is the 'object of the preposition'. When identifying gerund phrases, we're looking for the -ing form of the verb acting as a noun. In the sentence 'Brett earns his income by repairing cars,' 'repairing cars' is the phrase that tells us how Brett earns his income.
The preposition 'by' indicates that the following phrase is what he does to earn income, making 'repairing cars' the object of that preposition.