The correct answer is D) each.
The teacher distributed a piece of paper to each student.
"Each" is used to refer to every individual member of a group separately. Here, every student received one piece of paper individually, so "each" is correct. "A few" and "many" are incorrect as they refer to an indefinite number, not all individuals. "All" is grammatically incorrect here as it would require "all the students" (plural) not "all student."