Okay, I’ve been fiddling with this and I think I have figured it out. It matters greatly what type of increase you decide to use, and really it is a shame that the pattern doesn’t specify.
If you do a kfb (knit into front and back) increase, you are right you will increase each row by 3 stitches and end up with 24 stitches at the end of the 11 rows. You are using one of your existing stitches to create the increase by doing the kfb.
Now, if you did a M1 increase it would be entirely different. You are not using an existing stitch to make the increase and you will end up with 42 stitches by the end of 11 rows. So starting with 6 stitches…
Row 1: K1, M1, K1, M1, K1, M1, K1, M1, K1, M1, K1, M1 = 12 stitches
Row 2: Purl
Row 3: K2, M1, K2, M1, K2, M1, K2, M1, K2, M1, K2, M1 = 18 stitches
Row 4: Purl
Row 5: K3, M1, K3, M1, K3, M1, K3, M1, K3, M1, K3, M1 = 24 stitches
Row 6: Purl
Row 7: K4, M1, K4, M1, K4, M1, K4, M1, K4, M1, K4, M1 = 30 stitches
Row 8: Purl
Row 9: K5, M1, K5, M1, K5, M1, K5, M1, K5, M1, K5, M1 = 36 stitches
Row 10: Purl
Row 11: K6, M1, K6, M1, K6, M1, K6, M1, K6, M1, K6, M1 = 42 stitches