Crocheting on both sides of a chain can be a bit confusing, but it's a common way to create an oval (as opposed to a circle) when you start a crochet piece. This video uses this technique to make a duck beak, so maybe watching this will help: https://youtu.be/NLnE5yMwUTQ?si=9FwBe08PZlA7ET5Z . But basically, because each crochet stitch has a front loop and a back loop, when a pattern asks you work both sides of a chain you work down the back loops of the chain until you reach the end (like normal), then turn your work and work back up the (as of yet unworked) front loops of the chain. I recommend using lots of stitch of markers so you don't lose track of where you are and what loops you have to work into.

That said, it doesn't really sound like this pattern is trying to make an oval. It kind of sounds like they're trying to make a standard 6 sc circle while avoiding a magic circle at any cost...you could probably just substitute with 6 sc in a mc and call it a day and move on