Using the example in AAC:
http://www.allaboutcircuits.com/vol_1/chpt_10/7.html

Current across R1 = 6A - 1A = 5A
Couldn't it be 1A - 6A = -5A?
What determines the right direction?

 

The sign of the current in this case depends on the current direction convention you choose to use. The two competing current conventions have been discussed in several threads in this forum. The main thing that you need to do is chose one and thereafter be consistent.

Just keep in mind that since everyone has a choice between the two, not everyone will make the same choice.

hgmjr