The correct answer is A. On
Step-by-step explanation:
In grammar, prepositions are words used to show location, direction, etc, of nouns; prepositions include the words on, over, under, of, from, etc. The previous idea implies that for a preposition to be appropriate it needs to show the correct location, direction or relation of a previous noun.
According to this, in the sentence "Please place the silverware _____ the table" the most appropriate preposition is "on" considering this preposition is used to explain objects are above a surface, and it is expected silverware (cutlery) is found on the surface of the table.