Over and across are both prepositions that are used when someone needs to get to the other side of something, the other side of a bridge or a road, for instance.
Here are the rules:
1 When getting to the position on the other side means getting over something that is high(er), use “over”.
They climbed over the wall.
2 Use “across” when the position on the other side is reached on something flat, for instance when it’s a floor or the sea. “Across” is also used for a country.
The dancers moved across the ballroom.
We drove across the United States.
3 When rule 1 and 2 don’t apply, you can use both “over” and “across.” In that case, the position on the other side isn’t higher, or reached over something flat, and you can choose what to use.
The car drove across the bridge. (okay)
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