What could be the transmission loss per metre of using DC current for a low voltage solar system?
My question is: will this 6m additional wiring cause a significant
  loss of final output? Is there a formula that I can use to arrive at a
  numerical figure?


There is indeed a formula, but not in quite the sense that you seem to think. Wire has a per-meter resistance which is inversely proportional to the cross-sectional area of the wire, so asking what the voltage drop in a wire is requires that you know both what the wire size (gauge) is and what the expected current is.

And since Googling "wire resistance" will tell you everything you need to know, including links to calculators so you don't even need know the exact formulas being used, it seems that you haven't spent much effort on the question.

Simply saying that you have a 2kW system is pretty useless, since you have not specified the system's voltage (and therefor current). Furthermore, saying that one routing path will add an additional 6 meters doesn't help, since you haven't specified the length of the shorter path. For example, if the short path is 6 meters, the voltage drop on the longer path will be twice the shorter. If the short path is 24 meters, the difference will only be 25%.

Finally, you haven't specified what "significant" means. What is the voltage drop over the shorter path? How much of a greater drop will the inverter tolerate?

TL;DR - You've left out almost everything you need to include if you want an accurate answer.