Learn Farsi: ساک مسافرتی شما چقدر گنجایش دارد؟ - How much capacity does your travel bag have?

It comes from the verb gonjidan (to fit / to be contained). By taking the present stem gonj- and adding the suffix -âyesh, which is used to form verbal nouns indicating a state or quality, we get gonjâyesh (the state of fitting, meaning "capacity").

Why does the sentence use sâk instead of common words like kif or chamedân for "bag"?

These words refer to different types of luggage. A kif is a general bag (like a handbag, briefcase, or backpack), while a chamedân specifically refers to a rigid suitcase. Sâk refers to a soft-sided duffel or sports bag, making sâk-e mosâferati the exact term for a travel duffel.

How could I answer this question using the lesson's target phrase tâ hadd-e emkân (as much as possible)?

You could answer by saying Tâ hadd-e emkân jâ dârad (It has space to the extent possible) or Tâ hadd-e emkân vasileh tu-yesh jâ migirad (It fits items as much as possible). While the question asks for a measurement of gonjâyesh (capacity), you use the lesson's phrase as an adverbial expression to describe maxing out that space.

Could I ask this using the verb ast (is) instead of dârad (has)?

Yes, but you would need to change the subject of the sentence. You would say Gonjâyesh-e sâk-e mosâferati-ye shomâ cheghadr ast? (How much is the capacity of your travel bag?). Using (has) is often more natural in conversation because it allows the bag itself to be the active subject.