The cafe's employees were instructed that hand washing should ______ any contact with food or areas where food would be prepared.

The correct term to use in this context is "precede," which means to come before something in time or order. When employees are instructed that hand washing should precede any contact with food or food preparation areas, it emphasizes the necessity of washing hands before engaging in those activities. This is crucial for maintaining food safety and hygiene standards, as it helps prevent contamination.

The other terms listed do not fit appropriately in this context. "Proceed" implies moving forward and does not convey the intended meaning of doing something beforehand. "Preceed" is a common misspelling of "precede," and "preseed" is not relevant in this context, as it refers to something entirely different related to either farming or genetic engineering. Thus, the use of "precede" clearly communicates the importance of hand washing prior to handling food.