Let G be a planar Graph Such that every phase is bordered by exactly 3 edges
since graph conain odd length cycle, its chromatic no. X(G)>=3
so 2 can never be X(G), hence option a is correct.
Yes option a) is correct 2 is not possible because when a region consist exactly 3 edges means vertices joining them are adjacent and should be colored uniquely. You can also observe this with example below