Answer:
Your answer would be that the correct version of the sentence is the following one: My brother took out the garbage, and Motehr was very happy.
Step-by-step explanation:
You should capitalize words such as Mother, Father, Brother, Sister, Grandmother, Son, Daughter when they are used in place of the person's name. What is more, you should not capitalize them when they follow possessive pronouns (my, your, his, her, our). In the sentence above, Mother is capitalized because it is not preceded by any pronoun, while brother is not because it follows the possessive pronoun my.