The question is: ¿In how many ways the vertexes $P,Q,R,T,S$ and $W$ can be assigned to an hexagon, where all the sides are different?.
My doubt is if I have to use circular permutation or linear permutation. If we consider a regular hexagon, we can inscribe it in a circle. Therefore, the permutation will be circular. But in this case, I don't know how to proceed, and why I have to use one of them and not the other.
Since all of the sides are different, it is safe to assume that any non-identity relabeling will result in a different hexagon. Example: $PQRTSW$ is different from the circle permutation $WPQRTS$ because the sides between the vertices are all distinct. So, no matter what permutation you choose, there are no symmetries to worry about.
You use circular permutations when outcomes with rotational symmetries are consider identical outcomes.