Explanation:

- The sentence needs a preposition that fits with "written ___ the board."

- Option 1: "that" - This is not a preposition; it is a conjunction or relative pronoun.

- Option 2: "with" - This suggests an association or use of something, not the placement or inscription on an object.

- Option 3: "in" - This typically indicates being inside something, not applicable for surfaces like a board.

- Option 4: "on" - This is the correct preposition to describe something written on a surface such as a board.

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