Stage 6 parts are ultra-rare upgrades that give your car an edge against your opponents. They’re specific to each car model - so you can’t use a Ferrari 488 Spider stage 6 part on a Ferrari 458 Speciale.
If you have a stage 6 part for a car, you can fit it in the upgrade menu just like other stages, once that part is upgraded to stage 5 (eg, upgrades have to be in sequential order). They can be obtained from Donna in Rare Imports, by winning some events, and from stripping cars.
You can see the stage 6 parts you own in your garage by tapping the info “(i)” button on the right, then tapping inventory, then selecting the “stage 6 upgrades” tab.