This exercise stands for the concept of possessive adjectives that are used to point out ownership. So this type of adjectives agrees with the noun they modify. So they match the thing possessed not the possessor both in gender and number. The Table bellow shows the list of Short-form Possessive Adjectives.
(1) Correct answer
tu
familia is a feminine and singular noun, so we need to use tu that is the possessive adjective for the second person singular. In this way tu translates into your in English. Therefore the sentence Oye carina, tu familia es muy grande. Tienes muchos parientes translates into Hey Carina, your family is very big. You have a lot of relatives.
(2) Correct answer
mi
hermano is a masculine and singular noun, so we need to use mi that is the possessive adjective for the first person singular. So mi translates into my in English. Therefore Sí, es verdad. Aquí hay unas fotos. Mira, él es mi hermano Juan means Yes, it is true. There are some photos here. Look, he's my brother Juan.
(3) Correct answer
su
In this item, we have the word esposa that is a feminine and singular noun, so we need use su that is the possessive adjective for the third person singular here. So the su used here matches his in English. In this way, the question ¿Y ella es su esposa? translates into And is she his wife?
(4) Correct answer
sus
sobrinos is a masculine and plural noun, so we need to use sus that is the possessive adjective for the third person singular. In this way, the sus used here matches her in English. Therefore the sentence Sí. Y mis seis niños son sus sobrinos means Yes. And my six children are her nephews.
(5) Right answer
sus
abuelos is a masculine and plural noun, so we need to use sus that is the possessive adjective for the third person plural. So the sus used here matches their in English. Hence ¡Seis niños! ¿Y aquí están Juan y tú con sus abuelos? translates into Six children! And Juan and you are here with their grandparents
(6) Right answer
sus
primos is a masculine and plural noun, so we need to use nuestros that is the possessive adjective for the first person plural. In this way, nuestros matches our in English. Hence Sí, y en la foto estamos los dos con los hijos de los hermanos de mamá, nuestros dieciocho primos translates into Yes, and we are both in the pictures with the children of mom's brothers, our eighteen cousins.