Final answer:
The correct parts of speech for 'assign' and 'assignment' in a sentence are verb and noun, respectively, making option A the right choice.
Step-by-step explanation:
The parts of speech are foundational elements of English grammar, and each word in a sentence can be classified as a part of speech based on its use and function. The word "assign" typically functions as a verb, as it represents an action of giving tasks or responsibilities. On the other hand, "assignment" functions as a noun, since it is the thing that is being given or the task itself. Therefore, the correct option that makes the sentence structure make sense is A) Part of speech for "assign": verb, Part of speech for "assignment": noun.