Hmm. It almost sounds like they want you to work garter stitch, but they're calling the purl rounds 'reverse stockinette' and the knit rounds 'stockinette.'
If you wanted to work rev. st.st. in the round, you'd purl every round.
I suspect that what I said first was right.
(purl 1 round, k1 round) 3 times; then purl one round and bind off in knit.