"A teacher needs his luggage"

Translation: Mwalimu anahitaji mzigo wake

[SaraGangon]

I do not understand when we are using wake or yake. It does depend on what?

[Bmbwa]

It depends on the word class of the noun. This lesson is about the 3d and 4th class, better known as the m-/mi- class. (See fe https://discoverdiscomfort.com/swahili-noun-classes-cheat-sheet/). In class 3 (singular) a possesive (-ake) has the w- prefix => mti wake. in plural (class for) it takes the Y-prefix => miti yake.
For swahilj you need to learn all the classes and their prefixes by heart, but it goes quite easy when you get the hang of it ! For example, "my name": jina/majina is class 5 and 6, so it is jina langu and majina yangu

[DBall2814]

Does "mzigo" refer to a single piece of luggage while "mizigo" implies there are multiple pieces? "Luggage" can be used to describe both situations in English.

[thisisfourwords]

Yes that is correct.

[DBall2814]

Thanks!