The next day she pacified the teacher explaining her the reason for the previous day’s leave.

The correct answer is A. quietened.

To pacify someone means to make them calm or less angry. In this case, the student is trying to make the teacher calm by explaining the reason for her absence.

The other options are incorrect because they do not accurately describe the student’s actions.

• Option B, silenced, means to make someone
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  stop talking. The student is not trying to make the teacher stop talking, but rather to make her calm.
• Option C, pleased, means to make someone happy. The student is not trying to make the teacher happy, but rather to make her calm.
• Option D, flattered, means to make someone feel proud or pleased. The student is not trying to make the teacher feel proud or pleased, but rather to make her calm.