There's more than one way to solve the 4 band puzzle ring. Most solve it starting with the outside bands back to back. Alternatively, there's a way to solve it by setting them together as they are meant to be in the final solution and then weave the other two rings into their places.
0:00 Identifying the 4 different bands and how they interact
1:52 New solution - outside bands overlapping
4:12 Common solution - outside bands back-to-back
6:52 Showing the 1st solution again