Since, Graph 'G' has total $ (n+2+4+3)$ vertices and 'G' is connected with minimum no. of edges. So, G must be a tree. So, it should have $ (n+2+4+3-1)$ edges.
Now, According to Handshaking Lemma,
Sum of degrees of all the vertices in G = 2*No. of Edges in G
So, $n*1 + 2*2 + 4*3 + 3*4 = 2*(n+2+4+3-1)$