SUB-GRAPH : A sub-graph of G is a graph H such that V(H) $\subseteq$ V(G) and E(H) $\subseteq$ E(G)
In general , Normal Sub-graph is obtain by either you delete vertices or you delete Edges or both of them.
Induced sub-graph : is obtained by deleting a set of vertices only
Now , As we know that It's K(3,3) complete bi-partite graph
Total number of vertices = 6
So , In each and every vertices out 6 vertices we have a 2 choice 1) Either we deleted a vertex 2) Not deleted a vertex
therefore , total number of possible vertex induced sub-graphs = 26
Now , edge induced sub-graph is obtained by deleting a set of edges only
Total number of Edges in complete Bi-partite graph = 3 x 3 = 9
So , In each and every edges out 9 edges we have a 2 choice 1) Either we deleted a edges 2) Not deleted a edges
therefore, total number of possible edge induced sub-graphs = 29
now , they asked ,
X : Y = 26 : 29 = 1:23
therefore , X+Y = 1 + 23 = 9 ans