How to Solve a Complex Problem Using Euler's Path

The runtime of this algorithm is proportional to the number of edges and the number of nodes within this graph. The question is can I go to every single location on the board? Exactly one time not overlapping so I can't go back to the same location ever. And so how do you solve this one? Well, you essentially need to walk down every possible path So for simplicity sake, let's just say there's only two options when in reality there are much more options.