Learn Russian: Мы закончим упаковывать продукты после смены. - We will finish packing the products after the shift.

Even though the packing will be finished, Russian grammar requires that phase verbs like закончить (to finish), начать (to start), and продолжать (to continue) are always followed by an imperfective infinitive. The imperfective infinitive simply names the ongoing process, while the phase verb handles the finishing part.

Why is закончим perfective? Doesn't the rule say phase verbs use the imperfective?

The rule is that the second verb (the infinitive) must be imperfective. The phase verb itself can be either perfective or imperfective depending on the context. Here, закончим is perfective because the act of finishing is a single, completed event that will happen in the future.

What case is продукты in here? It looks like the nominative plural.

It is actually in the accusative case because it is the direct object being packed. However, because продукты (products or groceries) is an inanimate noun, its accusative plural form is exactly the same as its nominative plural form.

Why did смена (shift) change to смены?

The preposition после (after) always requires the genitive case. Since смена is a feminine noun ending in -а, we change the ending to -ы to form the genitive singular смены.