Learn Farsi: قوطی‌های فلزی باید به وسیله‌ی دستگاه تفکیک شوند. - The metal cans must be sorted by means of a machine.

Both are used to introduce the agent in a passive sentence, but به وسیله‌ی literally translates to 'by means of' or 'via the instrument of'. It is the most natural choice when the agent doing the action is a tool, instrument, or machine like دستگاه (dastgah). The word توسط is usually preferred when the action is done by a person, group, or organization.

Why is the verb شوند (shavand) in the subjunctive mood?

The word باید (bayad), meaning must or should, forces the verb that follows it into the subjunctive mood. Because this is a passive sentence ('must be sorted'), the passive helper verb شدن (shodan) is put into the present subjunctive form شوند to match the third-person plural subject قوطی‌ها (ghooti-ha).

How does the word فلزی (felezi) work here?

It is an adjective meaning 'metallic', formed by taking the noun فلز (felez - metal) and adding the common adjective-making suffix ی (-i). It connects to the plural noun قوطی‌ها (cans) using an ezafe. Since the plural noun ends in a vowel (alef), the ezafe is written and pronounced with a 'y' sound, giving us قوطی‌های فلزی.

Could we use جدا (joda) instead of تفکیک (tafkik) for 'sorted'?

Yes, you could say جدا شوند (joda shavand), which means 'be separated' and is very common in everyday speech. However, تفکیک specifically means separating into distinct categories, such as sorting recycling, mail, or data. It sounds a bit more technical, which fits perfectly when talking about an industrial process or sorting machine.