Final answer:
A double yellow line on a two-way road signifies that no passing is allowed in either direction, indicating a key traffic safety rule.
Step-by-step explanation:
A double yellow line down the center of a two-way road typically indicates that no passing is allowed in either direction. This traffic rule ensures the safety of all road users by preventing overtaking in areas where it is difficult to see oncoming traffic, such as on curves or hills. Therefore, the correct answer to what a double yellow line signifies is A) No passing allowed in either direction.