The pattern uses the Tunisian reverse stitch (R) and Tunisian knit stitch (K).
The larger size hook is the Tunisian hook for making the dishcloth, the smaller hook is for edging the finished dishcloth.
One colour of cotton is needed and the pattern states Coats or cotton worsted yarn:
150yds / 137m #661 Frosty Green
All the patterns in this book were designed not to curl.
Note that this isn’t the Tunisian honeycomb stitch pattern. It is simply named Honeycomb.