The brief
The 320i had its check engine light on and was misfiring, the engine stumbling and rough. He brought it in, the right move, leaving a misfire risks worse and costlier damage. The diagnosis pointed at the ignition coils, with the spark plugs due alongside. 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 light. The plugs wear too, the gap opening and the electrode rounding off, which makes a weak spark worse. A scan reads which cylinders are misfiring, and 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.
The diagnosis
A scan pulled the misfire codes and identified the misfiring cylinders, 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 BMW-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, the light staying off, and smooth power.
The outcome
Smooth idle, clean pull through the rev range, no misfires, no warning light, and fuel economy back where it should be. The 320i 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.