Right Purl Twist (RPT)
Like the Right Twist, the Right Purl Twist stitch creates a mock cable, crossing one stitch over the stitch to its right. With the RPT, however, the stitch in back is purled.
Working with the next two stitches on your left-hand needle, slip both together knitwise, like the beginning of a k2tog, which will reverse their order. Insert the left-hand needle into the two slipped stitches from left to right (so that the needle tips are pointing in opposite directions) and slip them back onto the left-hand needle. Now you can knit the new first stitch, then purl the second. Twist complete!
I haven't found a good video showing this approach to the LPT. If you know of one, please let me know!