Right answer: la
In Spanish grammar the article is a word that clearly indicates the gender and the number of the noun. Its function is to modify the noun it introduces.
The articles are as follows:
Variable Articles:
Defined Articles:
Singular Masculine: el
Singular Femenine: la
Plural Masculine: los
Plural Femenine: las
Indefinite Articles:
Singular Masculine: un/uno
Singular Femenine: una
Plural Masculine: unos
Plural Femenine: unas
Invariable Articles:
Neutral: Lo
Contractions: al (a+el) and del (de+el)
Now, in this sentence muchacha (girl) is a feminine singular noun.
We also have more information: she is not any girl, she is Juan's sister.
Therefore, we must use the defined article for singular femenine she (ella), which is la:
Esta muchacha es la hermana de Juan
This girl is Juan's sister
