Ok so you have:
Two vertices of degree 5
Two vertices of degree 3
Two vertices of degree 4
Now, calculate the sum of the degrees:
Sum of degrees = (2 * 5) + (2 * 3) + (2 * 4) = 10 + 6 + 8 = 24
Now, use the Handshaking Lemma to find the number of edges:
2 * (number of edges) = 24
Divide both sides by 2:
(number of edges) = 24 / 2 = 12
So, the number of edges in the graph is 12. Therefore, the correct answer is (b) 12.