In the graph above, I should count the number of possible spanning trees. Firstly, I looked at the cycles on the rightmost side and I have $2 \times 3$ for that half; but there are also cycles on the leftmost side of the graph and I concluded that are $2 \times 8$ spanning trees for that half. So there would be $96$ spanning trees but that seems to be an overcount. Any suggestions?
I drew the two parts of the graph as below. I removed self-loops (since they cannot be in the spanning tree) and bridges (since they must be in the spanning tree).
We can count the spanning trees in the following manner. The following $12$ set of edges form the spanning tree on the left half. $$\{{a,b,c\}},\{{a,b,d\}},\{{a,b,e\}},\{{a,b,f\}},\{{a,c,d\}},\{{a,c,e\}},\{{a,c,f\}},\{{b,c,d\}},\{{b,d,e\}},\{{b,d,f\}},\{{c,d,e\}},\{{c,d,f\}}.$$
For the right half, the following $5$ sets:
$$ \{{a,b\}},\{{a,c\}},\{{a,d\}},\{{b,c\}},\{{b,d\}}.$$
Since we can pick only one from each side for a valid spanning tree, we have $12*5=60$ spanning trees.