Question

What is the subject in the following sentence? After breakfast she needs to run a few errands.

Answer 1

She is the main word. After breakfast is a prepositional phrase, which depending on your teacher can be a subject. Needs is the verb, and run is the direct object

Answer 2

The main subject would be after breakfast. This is because the sentence is stating what she is doing after something. So the subject isn't breakfast or errands, it would be what is happening after breakfast.

Hope I could help :D