What you're doing is increasing in the middle for the thumb "gusset", the area where the thumb stitches will be.
Place marker between middle two stitches. (18 & 19th st) add two stitches, place another marker, Work in st st increasing 2 sts every other Row between marks until you have 14 stitches. Put these 14 on a holder for working thumb later.
Continue working st st adding 2 stitch under thumb once.
--Was I supposed to do all this while working the 6 rows in st st?
--With 38 stitches, wouldn't the middle two be 19th and 20th rather than 18th and 19th, or doesn't it matter?
--what exactly is meant by adding 2 stitch under thumb ?
You place the marker(s) so that you know where you'll be increasing stitches on the following rows & you won't lose track.
This is from a bit farther down in the directions where someone else asked the question. "Knit to just before the 18th stitch, place the marker, using the 18th stitch, inc 1. Use the next stitch, the 19th, and inc 1. Now place your second marker."
Then, following the directions, you'll be increasing on every other row until you have 14 sts BETWEEN the markers.
You'll put those stitches on a holder for use later.
Then, you'll knit across, and on the way back, after you've knit the 18? stitches you'll add 2 stitches and then knit the other 18. Then you'll have a one-piece section again to knit to the top of the mitten.
Hope this helps.