Hi Prajakta, what I said before must be all wrong.
With the pattern like that over the 4 rows you wouldn't want an increase. Also doing what I said didn't make any kind of a woven look of any kind, and not even interesting looking in the least.
So I started trying to figure out how to do what they say and not make an increase. I thought maybe hyperactive was going in the right direction when she said take the needle out, after all. Maybe you take the needle out and don't put it back loop you went "through", but put it back in the remaining loop and then knit the first stitch through the first loop.
But they don't seem to be saying that and if they wanted that you could accomplish the same thing by slipping over the first stitch and knitting the second and then knitting the first stitch through the back loop.
I tried that: skip the first stitch and knit the second, then go back and knit the first stitch through the back loop. If you do that and then purl a row and then offset it by knitting one and doing it again you at least get something interesting going on, and it looks a little "woven" maybe. But I have no idea if that is what they intend. Probably not.
You might try that and see what you think of it. Do you have a picture of what the finished stitch is supposed to look like that is good enough for us to see it very well?
The short answer is that I have no idea what they want you to do.