Some of the instructions are confusing, until you realize that the thing is knitted in garter stitch. The instructions refer to ridges and assume that the worker knows to turn and knit back to complete the ridges. If you follow the instructions precisely, you end up with an oddly misshapen thing but, if you knit back after picking up stitches along the side/edge and again after each decrease, it turns into a hood.

There is also one small error, the decreases are worked over 20 ridges, not 20 stitches. My interpretation of the instructions is as follows:

MUFFLER AND CAP COMBINED
Material
2 1/2 hanks Knitting Worsted. 1 pair Bone Needles No. 3;
1 Steel Needle No. 8
Cast on bone needles 60 sts (about 10 inches). Knit in ridges for 34 inches, then with steel needle, pick up 20 sts close to the needle on one side of end of scarf, and knit them on to the bone needle, having 80 sts on needle, knit back. This forms the cap part of muffler.
Knit 40 sts, k2tog, turn and knit back, for 20 ridges. Then k in ridges for 34 inches again, bind off.
Face Band. - Pick up 1 st from each ridge at front of cap, k1, p1 for 12 ridges, bind off, sew each end neatly to each side of scarf.

I slipped the first st of each row except for the last 9 ridges on one side before the shaping begins. Then I picked up loops in each of 9 purl bumps and 1 in the last slipped st, to maintain the slipped stitch edge throughout. Note that the decreases actually shape the back of the head and neck, not the front of the cap.