across and through                         
     Typical mistake:
     *It took us two hours to walk across the forest.
     
1  Across and through can both be used for a movement from one side of an area to another.
   across和through用来表示从平面的一端到另一端。

     Across is related to on - it suggests that the movement is on a surface.
     across与on有关——说明在表面上的移动
     Through is related to in - you move through a three-dimensional space, with things on all sides.
      through与in有关——穿过立体的空间

Compare:
比较：
       The lake was frozen, so we walked across the ice.（湖结冰了，我们从冰上过去）
       It took us two hours to walk through the forest.（我们用了两小时穿过树林）
       I walked across the square to the cafe.（我走过广场到咖啡店）
       I pushed through the crowds to the bar.（我挤过人群到酒吧）

2  Through is not used for a movement from one side to the other of something 'long and thin', like a river.
‘长而细’的东西，如：河，从其一端到另外一端，不用through
     She swam across the river. 她游过河(Not: *... through the river.)