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Nurses are responsible for assessing, planning, implementing, and evaluating patient care, while nurse's assistants usually assist with basic care tasks under the supervision of a nurse. Nurses generally hold more education and have a wider range of responsibilities compared to nursing assistants. Therefore, we should look for a task that requires basic care assistance and doesn't involve advanced knowledge or extensive medical decision-making.

A. Monitor NG drainage for color, character, and amount: This task involves understanding the medical significance of the different aspects of NG drainage. It might require more in-depth knowledge and the ability to make clinical judgments, which would likely fall under the nurse's responsibilities. B. Provide oral hygiene every two hours: Oral hygiene is a basic care task that does not require advanced medical knowledge. It's essential to maintain oral hygiene, especially for clients who are unable to do so themselves. This task seems appropriate for a nurse's assistant. C. Administer pain medication as appropriate: Administering medications often requires calculating dosages, understanding side effects, and evaluating patient responses, which are part of a nurse's responsibilities. D. Teach the client to assume the fetal position to help decrease her pain: Teaching a client requires a higher level of knowledge and understanding of the condition, making it more suitable for a nurse to handle.

From the analysis, option B (providing oral hygiene every two hours) is the most appropriate task for the nurse's assistant, as it falls under basic care without requiring advanced medical knowledge or clinical decision-making.