Breakdown of Компания закончила выпускать детали и начала их упаковывать.
и
and
их
them (acc)
компания
company
деталь
detail
Questions & Answers about Компания закончила выпускать детали и начала их упаковывать.
Why do we use the imperfective verbs выпускать and упаковывать here? Didn't the company completely finish and start these actions?
This is the golden rule of "phase verbs" (verbs about starting, continuing, or finishing an action). The infinitive that follows them must always be imperfective, no matter what. The phase verbs (закончила, начала) handle the idea of starting or finishing, while the infinitive just names the ongoing process.
Why are the phase verbs themselves (закончила and начала) in the perfective aspect?
While the infinitive following a phase verb must be imperfective, the phase verb itself can be either aspect! Here, we use perfective past-tense verbs because the company completed the specific events of finishing one phase and starting the next.
детали (parts) is the direct object of выпускать, so why isn't its ending changed for the accusative case?
It actually is in the accusative case! Деталь is an inanimate feminine noun ending in -ь. For inanimate nouns, the accusative plural is exactly the same as the nominative plural (детали).
Why does the pronoun их come before the verb упаковывать? Could we say начала упаковывать их?
You can definitely say начала упаковывать их, but putting short object pronouns like их (them) right before the infinitive is extremely common and often sounds more natural to a Russian ear.