"Esther anataka kujenga nyumba yake"

Translation: Esther wants to build her house

[RashmiPMohan]

esther wants to build his house - How can this be wrong

[AlistairDo7]

Why is it wake, as it's one house and that is the singular.

[AGreatUserName]

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).