The pattern should have an explanation in a "special stitches" section. I'll give you generic instructions; tailor them as needed.
As you work across the current row:
1. Instead of inserting your hook into the next stitch, insert it into the stitch in the third row below.
2. Yarn-over-hook and draw up a loop (as usual with sc), but draw it up long enough so your hook is even with the current row.*
*If your long loop is too short, the fabric will pucker vertically, trying to pull the current row down toward where you inserted your hook. So be generous, but not sloppy.
3. Then yarn-over-hook and draw through the two loops (as usual with sc).
The long loop will cover part of the fabric (on both sides), and the "stitch" part of the sc should be even with the rest of the current row.
4. This long sc will take the place of a regular sc and will appear slightly in front of the current row. (Some instructions may tell you to "skip" the stitch behind the long sc.) Work your next stitch in the _following_ current-row stitch, not the stitch behind the long sc.
You may want to use scrap yarn to make a practice piece so you can work out the technique before doing it on your "good" project.
Illustration and video available here:
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