There’s an extra “…return these 4 sts to the LH needle…” in the directions; delete the one in brackets:
Row 2; K2, P4 wrapping yarn twice around needle for each purl st, K2Row 3; P2, sl 4 WYIB, dropping extra 4 wraps; [return these 4 sts to LH needle,] pass the first 2 sts slipped over the last 2; return these 4sts to LH needle and k them in this crossed position, p2.
For the purl sts with wraps, you begin to purl as usual but instead of wrapping the yarn once around the needle and then slipping the st off the needle, bring the yarn around the needle a second time so that you have two wraps on the RH needle when you slip the st off the LH needle. Do this for 4 purl sts. Then on the next row, slip the wraps to the RH needle, letting one of the wraps drop so you end up with 4sts on the RH needle (not the 8 wraps).
On the RH needle slip the first 2sts over the 2 nearest the needle point and then slip all 4 of these sts (the 2 slipped sts and the 2 on the needle) to the LH needle and knit them. You’re just reversing the order of the sts so that you get the cross st pattern. It seems like a pretty pattern. Good luck with it!