Correct Answer: She asked her mother if she might have another slice of cake.

Solution : The correct choice will be the third option.

The steps of conversion are as follows:

• The reporting verb "said" is changed to "asked".
• "May have" (simple present tense) in the direct speech is changed to "might have" (simple past tense) in the reported speech.
• The connector "if" is used to introduce the reported clause in the case of yes or no questions.

Therefore, the correct answer will be: "She asked her mother if she might have another slice of cake."