Why can only the federal district court in State B order the woman to undergo a mental examination?

The correct answer is based on the principle of jurisdiction and venue in civil procedure. In the context of this question, a mental examination is often considered a procedural matter that falls under the court's authority to manage cases pending before it. Since the lawsuit is pending in State B, the federal district court in that state has the jurisdiction to make orders related to the proceedings, including the authority to require a mental examination of a party involved in the litigation.

The notion that the court where the case is pending has the power to enforce procedural rules, including examinations, is fundamental to ensuring that legal proceedings can be conducted effectively. Therefore, it is logical that only the court overseeing the case can issue such an order, as it is the court responsible for managing the litigation and ensuring all necessary examinations or procedures comply with the jurisdiction's rules and regulations.

While there may be rules or circumstances in other states affecting the ability to conduct a mental examination, the key factor here is that the case is actively being litigated in State B, and thus, the court in State B has the authority to handle matters arising from that litigation directly.