confused by this pattern

[cjsbmoore]

Here's the part that stumps me:

Next Row (RS): Cast on 46 (46, 44, 42, 40) sts, k to end of row - 172 (182, 190, 198, 206) sts at the end of this row.
Next Row: Cast on 46 (46, 44, 42, 40) sts, p to end of row - 218 (228, 234, 240, 246) sts at the end of this row.

What I'm not sure about is what cast-on method would work best at the BEGINNING of a row.....

Thanks in advance for your help!

[suzeeq]

Use the knit or cable cast on, just pretend the first st on the needle is the slipknot that you'd use if you were just starting something. Videos on the Cast on page.

[cjsbmoore]

So I would be casting on the new stitches, then knit them along with the rest of the stitches to the end of the row?

[suzeeq]

Yep, that's right.