A graph is having atleast XV/2 edges where X is the minimum degree of graph G and V is the number of vertices in graph G.
Hence according to condition,
E<=3V-6
XV/2<=3V-6
If we take x=2,3,4,5 some value of v will come.
For x=6 the condition is 0<=-6 , whuch is false
So X which is minimum degree cannot be 6.