@Lou,
I think I see what you’re getting at. From the website you linked, it uses:
punto al derecho: right side stitch, which is the knit stitch
and
punto al reves: i think this is what you called the left side, but really it translates to backwards stitch, which is the purl stitch.

basically in this pattern you will do the knit stitch all the way through (right side as you called it), then when you flip over your work you will do purl stitch all the way through (you called it left side, but really it’s the “back side” if we translate…. and generally it’s called the wrong side)

The key to working out what size your hat will be is “gauge”. I had no idea about gauge when I first started knitting and had some real knitting disasters as a result! The gauge will depend on the type of wool and the size of needles you use. One way to make a bigger hat with this pattern would be to simply choose thicker wool and fatter needles to knit with, it’ll look a little chunkier but still super cute. When you buy wool there is always a little guide on the label saying the gauge, ie. what size needles are recommended and how many stitches and rows it takes to make a certain size square. That should help you pick out a wool that’ll give you approximately the right hat size with 78 stitches.

I’m not sure what you mean by “right and left” based patterns. I’m no expert knitter myself… I usually knit a row, flip the knitting around and purl the next row. The “right side” of the knitting (ie. the side that will face outwards when worn) is always done with knit stitch in this pattern. The “wrong side” is always purl. Hope that helps?!

All the best, I hope the pattern works for you.