"She declares the house is hers."

Translation: Cô ấy tuyên bố ngôi nhà là của cô ấy.

[KyleMunz]

What is the difference between ngôi nhà and just nhà?

[TehVanarch]

Nhà just refers to houses in general but can also be used as a prefix for certain occupations like nhà báo (journalist), nhà chính trị (also known as chính trị gia, politician). When counting houses you can use ngôi or căn.