Do I need hard or soft brown sugar for brownies?
The in the US, light brown sugar always means the one in the bottom left.  The bottom right is dark brown sugar and has a higher molasses content. 
In the US, I typically see the 'brown sugar' in the upper right referred to as 'raw sugar' or the brand 'sugar in the raw'.  If you're using a US recipe, it needs the bottom left.

If you don't have any and its an ingredient like in brownies, try adding the molasses and sugar as separate ingredients.  1 Cup of sugar + 1 tablespoon of molasses is about the right ratio for light brown sugar.

If you can't get molasses...try dark corn syrup, honey, or depending on the flavor your want, maple syrup.  (A comment from @JasonTrue above mentions that beet syrup is an option as well, althought I haven't tried it.)