A) As the given graph is a planar graph and secondly we have only one connected component , so we can find the number of regions of the graph as :
r = e - n + 2
==> r = 12 - 9 + 2
==> r = 5
Out of these 4 will be closed regions and 1 as unbounded region..
Now as clear from the graph , all of 4 closed regions are cycles of 4 edges..
Now coming to your last question,
Say number of regions are "r" , then
No of edges which bound the region = 5r
But to remove double counting , we do no of edges = 5r / 2
Also say we have n vertices ,and the graph is 3 regular , so sum of degree = 3n which is also = 2e = 5r according to Handshaking Theorem..
So as the graph is planar so we have :
r = e - n + 2
==> 3n / 5 = (3n / 2) - n + 2
==> (3n / 5) - (n / 2) = 2
==> n = 20 vertices
So no of edges = 3n/2 = 30 edges