This is one of times you've got a collection of 'speculative' reconstructions; there are so many ways of reading the description or doing the dance. Webfeet's annotated descriptions are not committed to giving a 'correct original' (you can check the writeup of the Horse's Branle for an extreme case of this :-) and will quite happily select one variation on the basis that it works better in a typical eCeilidh environment.
The music is in '32 bars' and you can think of the dance in two halves, with 'A' music and with 'B' music.
... and head into a 'half figure 8'. Which means that they go behind the second couple - so the man turns behind the second woman and the woman turns behind the second man - and they need to get back to their own side and move 'down' the set one place.
If you draw your path on the floor with chalk, each person is drawing a half of a figure 8. Everyone ends up on the 'correct' side (so there is a line of men facing a line of women, just as you started) but the people you were dancing with are 'above you' in the set. You are still dancing with them but they have ended up closer to the band. ... Which works well but is a bit of guesswork and interpretation. There are other ways of looking at a very brief description, as discussed below
Which is sometimes called 'Right and Left through' or '4 changes of a circular hey'.
That's 'one change'. There are four of them and you are going to be marking out a square on the floor. You will get back to your partner at the end if the four changes..
Where are you? If you are first couple you ended up 'below' the second couple at the end of the 'half figure 8'; if you are the second couple, even if you didn't do a lot, you ended up 'above' the first couple.
That was the 'second change'.
It's a 'hey' as you are giving right hands, left hands, right, left. You are going in circles (or a square) with the first man and second woman going clockwise all the time and the first woman and second man going anticlockwise all the time.
At the end of the fourth change, the first man keeps going and starts the Hey with the first and second Women.
The above description has heys along the sides of the set - it is the first man crossing between the two women and dancing a hey on their side, the first woman crossing between the two men and dancing a hey on the mens side. Fine if there are a few of you in a large enough room but troublesome if the longways sets are packed tight. To avoid this, make the hey go across the set
The above description fits 32 bars of music; an A1, A2, B1 and B2. Cecil Sharp's reconstruction assumes all the second half movement fits into a single B. 24 bars in total with half the time for the cross over and half the time for the right and left through. The first couple have just finished their heys, the man with the two women (A1) and the woman with the two men (A2)..
Yes it's a rush...