The result to be utilised here is that K3,3(complete bipartite graph with 3 vertices in each partition) and k5(5 vertex complete graph) are simplest nonplaner graphs.
KURATOWSKI THEOREM: ANY GRAPH WHICH CONTAINS SUBGRAPHS HOMEOMORPHIC TO K3,3 OR K5 ARE NONPLANER (NOTE THAT IT IS AN IF AND ONLY IF CONDITION).
A graph is nonplanar iff we can turn it into K3,3 or K5 by:

Removing edges and vertices. (Making a subgraph.)

Collapsing degreetwo vertices into a single edge.

Applying an isomorphism to turn it into K3,3 or K5.
In the above graph ,
 remove vertex e
 put {a,d,g} in one partition
 put {b,c,f} in other partition
 remove edges between {a,d},{a,g},{g,d},{b,c},{b,f},{f,c}