Prove Hamilton and Euler - graphs

Question

i want to prove that if this is Hamilton or Euler.Euler is when there is even number (in this case there are 12 edges so it is,if it was 7 it will not be Euler).Hamilton is when Hamilton when every edge once and acne is going only once.In this graph.I draw it so i think it is

Answer 1

Your graph cannot be Eulerian; it would need to have at most $2$ verticies of odd valency. (your graph has $12$). Your graph is Hamiltonian as can be seen from the $\color{red}{\text{red}}$ path indicated above.