The correct answer is D) She means that her teacher is easily annoyed.
Explanation:
According to the <em>Cambridge Dictionary</em> the word tetchy means to become "easily angry, unhappy, or upset." In the phrase, the superlative form of the word is used (identified with <em>the</em> and the <em>-est</em> ending) which means that the speakers thinks her teacher is easily annoyed.
