The part on the first side that read:
Next row, knit 5, purl 20 (24, 28 ) knit 32 (36, 38 ), purl 20 (24, 28 ) knit 5. Next row, knit all across row would produce some stockinette as well. Because on one row you are knitting then purling, then knitting, then purling, then knitting and on the following row you are doing all knit stitches, you will have some stockinette in that section as well - the stitches that have knit on one side and purl on the other side.
The thing about this pattern that seems incomplete to me though is that it never specifies right side or wrong side. So on the part that I have bolded above, if you started that on the right side of your work, then you would actually end up with reverse stockinette because the purls would be on the right side (the side that will show) of your work. Do you see what I mean??
Don't be discouraged by this pattern being labeled 'easy' and it not seeming so easy after all. There are a lot of easy and well worded patterns out there that don't seem to leave as much to the imagination.