Throughout your game, you'll be racking up the miles in every game mode you play and every car collectively. To check your overall progress, visit one of your houses. Above your coffee table, you'll see an icon representing "Info", click this, then "MyTDULife". Now click to edit and select "Change" on any available option. Now hover over "Overall Progression" which is 4 across and 1 down on the list, represented by 3 bars.
Here you will see "Play Time", "Game Completion" and "Total distance driven", to which you can check your progress towards this achievement.