Learn Turkish: Yapacağı sunum için hazırlık yapıyor. - She is making preparations for the presentation she will give.

This is the future object relative participle you are currently learning. The root is yap (do/make). We add the future participle suffix -acak and then the 3rd person singular possessive suffix -ı ("her"). The k changes to ğ because it is followed by a vowel, making it yapacağı. Literally, it translates to "her future-making". Combined with sunum, it means "the presentation that she will make" (or "give" in natural English).

Why is the verb yapmak used for "giving" a presentation?

In English, we usually say "give a presentation", but Turkish uses the verb yapmak (to do/make) for this action. Therefore, sunum yapmak is the standard phrase for delivering a presentation.

Could we say hazırlanıyor instead of hazırlık yapıyor here?

Yes, but there is a slight difference in nuance. Hazırlanıyor is a reflexive verb meaning "she is getting ready" (often used for getting dressed or mentally preparing oneself). Hazırlık yapıyor uses the noun hazırlık (preparation) and means "she is making preparations" (such as researching, writing slides, or organizing materials), which fits the context of an upcoming presentation perfectly.

Why isn't there a pronoun like onun (her) or o (she) in this sentence?