Ha! I found your missunderstanding:
In stockinette Stitch, 16sts and 22 rows = 4" before felting. Cast on 22 stiches.
there are two different instructions / informations here...
In stockinette Stitch, 16sts and 22 rows = 4" before felting.
This is just your gauge: if you WOULD knit 16 stitches over 22 rows you would have a swatch of 4 inches by 4 inches.
You are supposed to try this out before you start you project. (so that your project becomes the same size as the pattern, adjustments can be made to the knitting or the pattern, if you need to)
then your pattern wants you to cast on 22 stitches for your project (not the swatch). your project (before felting) will be wider than 4 inches...
the information for the 4 by 4 inches is totally irrelevant for the acutal knitting.
For the knitting you cast on 22 stitches then you knit the first row. (I don't know what your pattern wants for row 2)