As there are 7 entries in degree sequence so ,
No of vertices = 7
Now applying Handshaking Theorem , we have
Sum of degrees = 2 * No of edges
==> 2 e = 3 * 6 + 6
==> e = 24 / 2 = 12
Now assuming the planarity and assuming only one connected component and hence applying Euler's formula we have :
No of faces = e - n + 2
= 12 - 7 + 2
In general ,
No of faces of a planar graph with k connected components = e - n + k + 1
So minimum possible number of faces for a planar graph will be 7 as found by having no of connected components = 1
So number of possible number of faces will be 6 with the given number of edges and vertices only if it is non planar..
With this assumption,
2) should be the correct answer..