Okay, this is how I had the conduit job explained to me (when they gave out hints through email), and it helped a lot.

Draw a 2 x 6 (columns x rows) rectangle of dots. Label the top right dot is M01E and the top left is M01W. Next row is M06E and M06W, etc.

The meridians (the north/south part of the juncture) are the rows. The parallels (the inner/outer part) are not the columns, but the "lines" separating the columns. So the inner parallel is in between the columns, and the outer parallel is the other side (it might help to fold the paper into a cylinder. Imagine that where the paper meets is the outer parallel).

Then, start from one of the broken conduits (since that will limit how you can configure the junctures), and draw it out on the paper. I seem to remember that a pattern emerges pretty quickly. Then try it out in the game and see if it works!