Answer
IUPAC: 6,6-dimethylcyclohexa-2,4-dienone
Common name: No common name
Work Step by Step
The carbon attached to the ketone is carbon 1. So the 2 methyls are attached to carbon 6. There is a double bond at carbon 2 and one at 4, and there is a ketone so it's a dienone. When all these parts are arranged the name of the molecule is 6,6-dimethylcyclohexa-2,4-dienone.
There is no common name.