The brief
The X6 was misfiring, the engine stumbling and rough with the check engine light on. The easy assumption is the ignition coils, but you don't always point the finger there, a misfire can come from the fuel side too. He brought it in for a proper diagnosis. A misfire is a cylinder not burning cleanly, and that can be a weak spark from a coil, a worn plug, a vacuum leak, or a fuel injector that's not delivering its fuel properly, either leaking, sticking, or not atomising. A BMW diagnostic handset reads which cylinder is misfiring and helps narrow down whether it's spark or fuel. Here it pointed at the fuel side, a faulty injector on the misfiring cylinder. A failed injector doesn't recover, so it needs replacing, and on these the new injector has to be coded to the engine.
The diagnosis
A diagnostic scan with the BMW handset pulled the misfire to a specific cylinder, and tests showed the spark on that cylinder was fine, so the fault was the fuel injector, not delivering its fuel cleanly. The coils, the plugs and the rest of the engine checked out, it was that one injector. That's an injector replacement, you don't rebuild it on the car, so the call was a new genuine BMW-spec injector, fitted, coded to the engine, and the codes cleared.
The work
The old faulty fuel injector was removed, the bore and seat cleaned up, and a new genuine BMW-spec injector fitted with fresh seals. The new injector was coded to the engine so the management uses its correct calibration, the misfire codes cleared, and the engine's adaptations reset so it could relearn against a clean injector. A road test confirmed a steady idle, no misfires, the light staying off, and smooth power.
The outcome
Smooth idle, clean pull through the rev range, no misfires, no warning light, and the engine running properly again. The X6 went home running properly. A faulty injector causes a misfire just as a bad coil does, so a proper diagnosis pointed at the right part, and changing the injector and coding it in put the running right rather than throwing coils at it.