So five nodes have exactly four sides.
A * * * in the picture has six faces, and two faces need to be removed.
However, the deleted two items cannot disconnect the generated graph.
So in the photo,
{1, 2}, {3,4} and {5,6} cannot be deleted at the same time.
Therefore, there are C (6,2)-3 =15-3 =12 methods for spanning trees.