You should have 8 rows of 2x2 rib. We're going to switch to the 5 mm needles as we knit our first row. I always forget to switch needles and have found it useful to immediately put away the needles I'm not going to be using anymore. Otherwise, 6 rows in, I'll find out I've been using two 5 mm needles and three 4.5 mm ones!
Here is the pattern:
Row 9: Using the 5 mm needles *K4, p4 repeat from * to end
Rows 10-12: Repeat row 9
Row 13: *P4, k4 repeat from * to end
Rows 14-16: Repeat row 13
Here is the pattern written out in long form:
Using a 5 mm needles, at the beginning of the next (9th) row, Knit 4 stitches. Bring the yarn to the front and purl 4 stitches. Continue knitting 4 then purling 4 until the end of the row. NOTE: each time a 4.5 mm needles is freed of its stitches, put it away and grab a 5 mm needle instead. Keep knitting in the knit 4 then purl 4 pattern until you have completed 4 rows. You should have squares of knitting that are 4 stitches across and 4 up.
On the next (13th) row, purl 4 stitches. Bring the yarn to the back and knit 4 stitches. Continue knitting in the purl 4 then knit 4 pattern until you have completed 4 rows. Then you will return to the knit 4, purl 4 pattern and repeat these 8 rows.
Here are the Videos:
The first four rows of basket-weave:
And the second four rows of basket-weave:
Keep going in basket-weave until you have 3 or 4 repeats of the 8 row pattern depending on how big your head is and how big you want your hat. When I first started knitting, I knit quite a few hats that were comically small. I kept thinking that the hats would be too big so I would start decreasing and they would end up not even hitting the tops of my ears. So keep knitting until your hat is at a comfortable ear level and leaves a gap of only a few inches on the top of your head.
Coming soon.... Decreasing!