To solve this question, the user needs to know the correct usage of pronouns and their corresponding gender.

Now, let's go through each option and explain why it is right or wrong:

A. his: This option is incorrect because "his" is a possessive pronoun used for males. In this sentence, the subject is a female, so the possessive pronoun should be changed to match her gender.

B. she: This option is incorrect because "she" is not a possessive pronoun. It is a subject pronoun used to refer to females.

C. her: This option is correct. "Her" is a possessive pronoun used to refer to a female subject. In this sentence, "her" correctly refers to the female subject who has an apple in her hand.

D. my: This option is incorrect because "my" is a possessive pronoun used to refer to the speaker. In this sentence, the subject is not the speaker, so this option is incorrect.

The Answer is: C.