Learn Turkish: Bebek uyumuyor çünkü oyuncağını düşürdü. - The baby is not sleeping because he dropped his toy.

This is the witnessed past tense suffix for the third person (he/she/it). Because the last vowel in the verb root düşür- (to drop) is ü, four-way vowel harmony rules mean the suffix must also use ü, making it -dü.

Is düşürdü related to the verb düşmek (to fall)?

Yes! düşmek means to fall, but changing it to düşürmek makes it mean to drop (to cause to fall). So düştü would mean the baby fell, while düşürdü means the baby dropped something.

The dictionary says toy is oyuncak. Why is there a ğ in oyuncağını?

This is a rule called consonant mutation. When a Turkish word ends in k and receives a suffix starting with a vowel, the k almost always softens into a ğ so it is easier to pronounce.

What is happening with the -ını at the end of oyuncağını?

It is actually two suffixes joined by a buffer letter. The first -ı is the possessive suffix meaning his. The -n- is a buffer consonant. The final -ı is the accusative case suffix, showing that the toy is the direct object being dropped.