Eulerian and Hamiltonian Graphs · Hard problem

A sensor network has six stations $1,2,\dots,6$. Cables run around a hexagon, $12, 23, 34, 45, 56, 61$, and also along the three long diagonals $14, 25, 36$. A technician wants to test every cable by walking a single closed route that crosses each cable exactly once; where needed, a cable may be duplicated for the day so the route can cross it twice. What is the minimum number of cables that must be duplicated?