Here e<=2n-4 condition for graph containing no triangle(bi-partite) can be used for checking non-planar. But doesn't always work, can only be used in contrapositive sense.
(Simple & Planar & No Triangle → e<=2n-4) (→ is implication)
e=9 and n=6,
e<=2n-4
9<=2*6-4
9<=8 is false, So LHS should also be false.
We know Graph is simple and contains No triangle, then planar condition has to be false , making G1 non-planar.