What are some non planar graphs whose sequence is $(4\,4\,3\,3\,3\,3)$?

Question

I know that in order for the $6$-vertex graph to be non planar, it needs to contain more than $12$ edges. I tried drawing some picture to find the graph, but run out of ideas. It's easy to find the planar one, but not the non planar one.

Any ideas?

Answer 1

I'm not sure what you mean by your first sentence - the complete bipartite graph $K_{3,3}$ is non-planar and it only has $9$ edges. And in fact (hint) if you make a small modification to this graph I think you will have an answer to your question.