There is a standard method for checking whether a simple connected graph has an Eulerian Circuit. A simple connected graph has an Eulerian circuit iff the degree of every vertex is even. Then, you can just go ahead and on such a small graph construct one. For example, ABFECDEGCBGFA.
However, all you need for an Eulerian path is that at least n-2 vertices have even degree where n is the number of vertices in your graph. Then , you start at a vertex with odd degree and end at one as well.
There is a standard method for checking whether a simple connected graph has an Eulerian Circuit. A simple connected graph has an Eulerian circuit iff the degree of every vertex is even. Then, you can just go ahead and on such a small graph construct one. For example, ABFECDEGCBGFA.
However, all you need for an Eulerian path is that at least n-2 vertices have even degree where n is the number of vertices in your graph. Then , you start at a vertex with odd degree and end at one as well.