What you need to do is:
Put your yarn to the front, ready to purl.
Put the right needle through two of the stitches on the left needle (instead of one that you'd do for a normal purl)
Purl the stitches, but leave out the last bit, where you flip the stitches off the needle.
Put the yarn to the back, ready to knit.
Put the right needle through the two stitches on the left needle which you just purled (instead of one that you'd do for a normal knit)
Knit the stitches completely, including flipping them off the needle.
I thought that would look less complicated. Hope it's not too confusing.