You could use Euler's polyhedron formula:
[tex]V-E+F=2[/tex]
where V - numbers of vertices, E - numbers of edges and F - numbers of faces. In this case we have V = 6 and F = 8 so:
[tex]V-E+F=2\\\\6-E+8=2\\\\E=6+8-2\\\\\boxed{E=12}[/tex]
Polyhedron has 12 edges.
