"Esther anataka kujenga nyumba yake"
Translation:Esther wants to build her house
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It is yake because it is one house.
nyumba yake = her/his house
nyumba zake = her/his houses
The forms of the possessives depend on the class of the thing possessed, not the possessor. Nyumba is an N/N noun (classes 9/10), so it gets y- in singular and z- in plural.
Wake would be used for people (e.g. malimu wake, BUT dada yake) and inanimate nouns in the m- and u- classes (e.g. mtumbwi wake, uso wake).