Learn Russian: Завод продолжает выпускать самые новые автомобили. - The factory continues to produce the newest cars.

This is the core rule for phase verbs (verbs of beginning, continuing, and ending). Verbs like продолжать (to continue), начинать (to begin), and заканчивать (to finish) must always be followed by an imperfective infinitive. That is because they focus on the ongoing process of an action, not a single completed event.

How do we say 'the newest' in this sentence?

We use the word самый (the most) combined with the adjective. Here, самые новые literally means 'the most new' or 'the newest'. Both самый and the main adjective must match the noun they describe in case, number, and gender. Here they are plural and accusative to match автомобили.

Выпускать means 'to produce' here, but what is its literal meaning?

The verb выпускать literally means 'to let out' or 'to release'. The prefix вы- means 'out', and пускать means 'to let' or 'to allow'. It is widely used for a factory putting out products, a publisher releasing a book, or even literally letting a pet out of a house.

Since автомобили is the direct object (Accusative case), why do its endings look like the dictionary form?

Because автомобили (cars) are inanimate. In the plural, inanimate nouns in the Accusative case look exactly like they do in the Nominative case. The adjectives modifying them, like самые новые, also keep their Nominative plural forms. If the noun were animate, both the noun and the adjectives would take Genitive endings instead.