Planar Graphs · Hard problem

Take $K_5$ on vertices $1,\ldots,5$ and subdivide its three edges $12$, $13$, $23$, each by inserting one new degree-$2$ vertex ($6$ on edge $12$, $7$ on edge $13$, $8$ on edge $23$). For this graph $G$ (now on $8$ vertices), find $(3V-6) - E$.