You will need a US10.5(6.5mm) 16” circular needle and a set of US10.5(6.5mm) DPNs.
From the book: “This cute hat has a garter-stitch border and an oh-so-cute and feminine scalloped edge. Inspiration for the I-cord scallop is from Knitting Over the Edge, by Nicky Epstein. Knitted with Cashmerino Superchunky, it is soft and warm. And oh so fast to knit!”
Errata: The book incorrectly lists the row gauge as 4.5 rows/4” - that is the gauge to the inch. The correct row gauge should read 18 rows = 4”.