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Step 2 - Solve the Edges

This is how to pair the edges of a 4x4x4 two at a time.

Algorithms

In general, pairing is pretty easy. There is no one algorithm that you can use because you should be able to replace a set of paired edges with another pair from almost any other position, but this will give you the basic idea. In general, you make the first pair with a Uw', take the pair out and replace it with the dedge that belongs with the other dedge in the FL slot, and make the second pair (and restore the centers) with Uw.

Diagram "Algorithm" Comments
Uw' (R U' R') Uw This is a VERY BASIC example of how to pair two sets of edges. Remember that the edges could be in more than one position, so be flexible here. I use the FL and FR edge positions to pair. Identify where the dedge is that will match up with the bottom dedge in the FL position. If this dedge is in the BR or BL positions, move it so that it is in any other position. Notice that the Uw' completes a pair in the FR position. Then R takes out the pair, U' replaces it with another set of edges, and R' inserts the new set of edges into the FR position. Finally, Uw restores the centers and pairs the second pair in the FL position. Depending on the position of the edge you'll be inserting, you will use a different combination of moves between Uw' and Uw.
Uw' (F R' F' R) Uw This is the same concept as the above case except because of the orientation of the edge, it needs to be inserted with a sledgehammer instead.

Special Cases

Sometimes we will need to swap pieces in only two edge positions instead of three. If this happens for the last two edges, we can just apply the algorithm. There is also a nice shortcut here if they are not the last two edges to pair.

Uw' (R U' R') Uw2 (L' U' L) Uw' This is a special case that will allow you to actually solve three (or sometimes four) pairs instead of just two. I used to think of this as a hindrance but it's actually a pretty neat solution to an irregularity. Here, the Uw' makes the first pair, R U' R' takes out the pair and replaces it with an unsolved edge, Uw2 completes the second pair, L' U' L takes out the second pair and replaces it with the counterpart to the third pair, and Uw' completes the final pair and restores the centers. Note that depending on where the third pair is, you will not quite follow this algorithm. Again, just make sure that the two pieces for the third pair are not in the BL and BR positions before pairing.
Uw' R U R' F R' F' R Uw If there are only two pairs left to solve, line up the edges so that they match across from each other (so that a Uw' or Dw would NOT pair them) and perform this algorithm.