Learn Hardcore Turkish: Toz bezini kullanarak rafları temizlemem gerekiyor. - I need to clean the shelves using a dust cloth.

The -i here is the accusative case marker (with vowel harmony: -ı/-i/-u/-ü). In Turkish, when a direct object is definite or specific, you mark it with the accusative. By saying toz bezini, you’re talking about the dust cloth you have (not just any dust cloth), so you add -i to bez (cloth).

Why do we say toz bezini instead of just toz bezi?

Without the accusative (toz bezi), the object is indefinite or generic (“a dust cloth” or “dust cloths in general”). Adding -i (to get toz bezini) makes it definite (“the dust cloth”). Since you need a specific cloth to clean the shelves, you use the accusative.

What does the -arak suffix in kullanarak mean, and why -arak and not -erek?

-arak/-erek is the “instrumental/adverbial participle” suffix, equivalent to English -ing in “by doing…” or “while doing….” You attach it to a verb stem to show the means or method. Due to vowel harmony, kullan (with back vowels u, a) takes -arak, so kullan + -arak = kullanarak (“by using”). If the stem had front vowels, you would use -erek.

Why is kullanarak not just ile kullanmak or kullanarak ile?

You can say toz bezi ile rafları temizlemek (“to clean the shelves with a dust cloth”), but that uses ile (“with”) plus the infinitive. kullanarak is more dynamic: “by using.” It embeds the method directly in the sentence as a participle. Both are correct, but kullanarak emphasizes the action of using.

What is happening in temizlemem gerekiyor? Why not temizlemeliyim?

Turkish offers two main ways to express necessity:

Verb-stem + ‑meli/-malı (e.g. temizlemeliyim) is a modal suffix meaning “I must/should clean.”
Temizleme-m gerekiyor literally “my cleaning is necessary,” using the verb gerekmek (“to be necessary”) plus a nominalized verb.

Using gerekiyor is slightly more formal or objective (“It’s necessary that I clean…”), while -meli is more like giving advice or expressing your own obligation.

Why does temizlemem end in -m?

Here temizleme is the nominalization of temizle- (“to clean”). To link it to gerekmek, you need a possessor: “my cleaning.” The -m is the first-person singular possessive on that noun. So literally you have:
temizleme-m (my cleaning) + gerekiyor (is necessary) → “my cleaning is necessary,” i.e. “I need to clean.”

How would you change the sentence to we need to clean the shelves using the dust cloth?

Simply adjust the possessive on the nominalized verb to first-person plural:
Toz bezini kullanarak rafları temizlememiz gerekiyor.
Here temizleme-miz is “our cleaning,” so “our cleaning is necessary,” i.e. “we need to clean.”

Is the word order in Toz bezini kullanarak rafları temizlemem gerekiyor fixed? Could I put rafları before toz bezini?

Turkish word order is fairly flexible, though the verb (or predicate) usually comes at the end. You can swap the two adverbial/object phrases for emphasis:
Rafları toz bezini kullanarak temizlemem gerekiyor.
Both sentences mean the same; choosing which phrase comes first depends on what you want to highlight.