The brief
The A3 had gone rough: misfiring, hesitating on acceleration, idling unevenly. He brought it in, and the maintenance check found the cause, ignition coils on the way out, with the spark plugs due alongside them. Each cylinder has a coil that delivers the high-voltage spark and a plug that fires it. The coils heat-cycle and wear, and when one starts breaking down the spark gets weak or intermittent, which is the misfire and the rough idle. The plugs wear too, the gap opening and the electrode rounding off, which makes a weak spark worse. The smart move when you find a bad coil is to do all the coils, not just the suspected one, and the plugs with them, because they've all done the same miles and you don't want to be back here for the next one. So it was a full coil set and a full plug set.
The diagnosis
Diagnostics confirmed misfire counts, and a check found a coil breaking down with the others tired from the same mileage, and the plugs worn, the gaps opened up past spec. The injectors and the rest of the engine checked out, it was the ignition side. So it was a full ignition coil set and a full spark plug set together, every cylinder getting fresh hardware so they all fire the same.
The work
The old ignition coils and spark plugs were removed, and a full set of new genuine Audi-spec coils and a full set of new plugs fitted, the plugs gapped and torqued, the coils seated properly. The misfire codes were cleared and the engine's adaptations reset so it could relearn on a clean ignition system. A road test confirmed a steady idle, no misfires, no hesitation, and smooth power.
The outcome
Smooth idle, clean pull through the rev range, no misfires, no hesitation, and fuel economy back where it should be. The A3 went home running properly again. A failing coil only takes the others and the plugs down with it the longer it's left, so doing both as full sets put the ignition right in one go, no coming back for the next one.