Learn Farsi: صندوقچه‌ی کوچک از مقوا ساخته می‌شود.

It uses the diminutive suffix -چه (-che) from this lesson. It attaches to the noun صندوق (sanduq), meaning "box" or "chest", to create صندوقچه (sanduqche), which means a "small chest" or "casket".

If صندوقچه already means "small chest", why does the sentence add کوچک (kuchak), which also means "small"?

In Farsi, it is very common to use a diminutive suffix like -چه (-che) alongside the adjective کوچک (kuchak) for emphasis. It sounds perfectly natural to native speakers, even though it literally translates to "the small small-chest".

Why is there an extra ی attached to the end of صندوقچه‌ی?

That is the Ezafe, which links the noun to its adjective کوچک (kuchak). Because صندوقچه (sanduqche) ends in a silent "h" (acting as an "e" vowel sound), the Ezafe is written as ی to connect the words smoothly. It is pronounced "sanduqche-ye".

How does the verb ساخته می‌شود (sâkhte mishavad) mean "is made"?

This is the passive voice. It is formed using the past participle of the verb ساختن (sâkhtan, "to make"), which is ساخته (sâkhte), followed by a conjugated form of the helper verb شدن (shodan, "to become"). Here, می‌شود is the present tense, so the phrase literally means "becomes made".