Learn Turkish: Çavuş koğuşu kontrol edebilir. - The sergeant can check the dormitory.

It is the accusative case suffix. The base word is koğuş (dormitory). Because the sergeant is checking a specific dormitory ("the" dormitory), it takes the definite direct object ending. Following 4-way vowel harmony, the suffix is -u.

How does the word edebilir break down?

The base helper verb is etmek (to do). First, the t changes to a d because we are adding a suffix that starts with a vowel. Then we add the ability suffix -ebil (can / able to), and finally the aorist tense suffix -ir, giving us edebilir (he/she/it can do).

Why is the verb "to check" written as two words (kontrol edebilir)?

In Turkish, many verbs are formed by combining a noun with a helper verb like etmek (to do). Here, the word kontrol (control) pairs with etmek, so "to check" is literally "to do control" (kontrol etmek).

Why is the aorist tense (-ir) used here instead of the continuous tense (-iyor)?

While kontrol edebiliyor (is able to check right now) is grammatically correct, the aorist tense (edebilir) is the standard and most common way to express general ability or possibility in Turkish, translating perfectly to the English "can check" or "might check".