What is the first order predicate calculus statement equivalent to the following?
"Every teacher is liked by some student"
Answer is (B). In simpler way we can say If $X$ is a teacher then there exists some $Y$ who is a student and likes $X$.
(A) choice: If $X$ is a teacher, then there exists a $Y$ such that if $Y$ is a student, then $Y$ likes $X$.
(C) choice: There exist a student who likes all teachers.
(D) choice: Everyone is a teacher and there exists a $Y$ such that if $Y$ is student then $y$ likes $X$. Assuming one cannot be both student and teacher at same time, this just means, everyone is a teacher.
"Every teacher is liked by some student" is equivalent to If (for all people ) person is the teacher then liked by some student.
Option B say exactly that. But Option D says (for all people ) person is the teacher and liked by some student.