The correct option is B both, and
The given sentence expresses two possibilities in the way the students have esteem/approval for their teacher, they "respected" and "admired" her as she was friendly. The option that best suits the sentence is 'both...and' as it means that both the possibilities are true, hence option C is correct. Because a teacher is friendly, you develop positive impressions of her, and 'respect' and 'admire' are both in the positive sense, hence 'neither...nor' will not be used, as it expresses negative, and not positive aspects. Hence option A is incorrect. 'Either...or' is used in a sentence when there is a choice between two possibilities, and both cannot be chosen. Since there is no choice in the given sentence, the students can admire as well as respect their teacher, option B is incorrect. 'Though...yet' is used in a sentence when there are alternate or opposite possibilities, whereas the possibilities in the sentence are not opposite, they're both impressions made of a person in the positive sense, hence option C is incorrect.