Pattern recommends double-pointed needles. It refers to using a double-pointed needle as a cable needle.

Gauge:
13 sts = 2 inches on US no. 4 needles
6 sts = 1 inch on US no. 5 needles

Needles:
Children’s: 1 set each dp needles US nos. 2 and 4
Women’s: 1 set each dp needles US nos. 3 and 5