"The soldier runs over the wall."
Translation:De soldaat rent over de muur heen.
This ("heen") has been tricky for me, too. I believe that using "heen" makes it clear that the soldier is running over the wall, from one side of it to the other. The word here, I think, is "overheen" and it separates to enclose the thing over which the action takes place. "Overheen" (or "over ... heen") adds more information than "over" by expressing space, direction, or completeness. "Over a wall" is anywhere on or above a wall. "Over een muur heen" is (perhaps loosely here) over and across a wall.
Van Dale defines "heen" as "hiervandaan; ergens naartoe." So "overheen" is from one place to another by way of a route that is situated higher. Compare onderheen (from one place to another by way of a route that is situated lower). On the other hand "over" and "onder" mean, merely, a place higher than or lower than, respectively.