When moving from one side to another while surrounded by an environment, use "through" and not "across."
When moving from one side to another while surrounded by an environment, use "through" and not "across:"
The hikers made their way through the dense forest.
The hikers made their way across the dense forest.
Use "across" (not "through") to describe movement over a flat area or surface from one point to another:
The artist painted broad strokes across the canvas.
The artist painted broad strokes through the canvas
Use "through" to stress being surrounded by something. Use "across" to indicate movement from one side to the other of something with limits or sides:
"Across" refers to reaching the opposite side of an area, or traversing the extent of something with clear boundaries, such as a river, city, or street:
Olivia had to drive across the city to get to the new art gallery that everyone's talking about
The old bridge that stretches across the river is still used by locals to reach the market on the other side.
Alice looked both ways before walking across the street to meet her friend waiting on the sidewalk.
We also use across to describe the measurement from one side to another, often indicating the breadth of an object or space:
The new dining table was quite wide, measuring 90 inches across, which made it perfect for large family gatherings.
When talking about movement 'in something', such as a tunnel, fog, forest, etc. we typically use "through:"
The train moved slowly through the tunnel.
However, there are sentences where "through" and "across" could be used interchangeably, typically when the distinction between moving within an enclosed space and moving over a surface isn't clear-cut or is less important:
We walked through/across the park.
The bridge goes through/across the lake.
