I’m not sure where the increases/cast ons go for that very first part. If it says to cast on 6 and then the chart begins with 13, that is not telling you exactly what to do. I’m guessing you start at the bottom of the stocking because you shouldn’t have a lot of shaping at the top. I guess you will just have to use your head on that first part. Look at the picture of the stocking and at the chart. Which way is the shaping going? If you start with 6 and go to 13 you need 7 increases. If you kfb in each stitch it would only give you 12. So it is not that.
Working with moss or seed stitch (I believe it is two names for the same thing, that is why it is confusing) makes it a little more exacting. You can’t really increase in the middle of a seed stitch pattern and not foul it up. So you need to increase on the outside edges all the time. Since it doesn’t tell you what to do, here is what I think I would try. Cast on 6. Purl one row. Next row: (K1, P1) into the first stitch, * then make one as a knit using the strand between stitches, p1; repeat from the * to last st. M1 kw again, (p1,k1) into the last stitch. This gets you from 6 to 13 and establishes the k1, p1 across.
On the next row just work each stitch as the opposite of what it is. So it will be k1, p1 across.
(That is the way to work it if you want the stitches added to be added evenly across, but if they all go on the same side or something that would be different. )
On the next row, going from 13 to 17 are those added 2 on each side? Or all on the same side? The chart should show by having stitches extend where they want them. Either way I think I would add them the same way. If 2 or all four go at the beginning I would use a knitted cast on to add the stitches and then looking ahead at the pattern as it is going, knit or purl those stitches so that they are in the correct sequence. Pattern across. If you add 2 or 4 at the end of the row, I would work to the end and then then turn and knit on the 2 or 4. So they really end up at the beginning of the next row. Work them in sequence as needed on the return row.
So for the type of increases. If only one increase is needed at one or each end I would K1, P1, or P1 K1 into the first stitch (whatever works with the sequence). If you need two or more I suggest a knitted on cast on and then work them in sequence.
Good luck. Let me know if any of this helped at all. If I am totally not getting the picture, let me know and maybe I can try again with new input added.