The brief
The 216i had a problem at the back: poor or absent airflow from the rear vents, the rear fan cutting in and out, an unusual noise from it, and not much cooling reaching the back seats even with the front working fine. He brought it in. That's the rear aircon blower. On cars with rear vents there's a separate blower motor that pushes the cooled air to the back, and it has a fan, a motor and a speed control. The motor's bearings wear and get noisy, the fan can foul on debris, and the control can go flaky, so the airflow drops off and stutters. When the blower unit's reached that state, you replace the whole assembly, fitting new properly working parts rather than chasing a worn motor that's only going to keep deteriorating.
The diagnosis
A check confirmed it, the rear blower motor was worn, drawing badly and noisy, the airflow weak and inconsistent because the fan wasn't spinning up properly. The ducting and the rear aircon controls checked out, it was the blower unit itself. That's a blower replacement, you don't rebuild the motor on the car, so the call was a complete rear blower assembly, fitted and tested.
The work
The trim came off to reach the rear blower, the failed unit unbolted and removed, and a new genuine BMW-spec rear blower assembly fitted, connected up, the ducting checked clear, and the trim refitted. The rear aircon was run through its speeds to confirm the new blower spun up cleanly and pushed proper airflow. A check confirmed strong, steady airflow from the rear vents, cold air reaching the back, and no noise.
The outcome
Strong, steady airflow from the rear vents, cold air reaching the back seats, no stutter, and no noise from the blower. The 216i went home with the rear cooling sorted. A worn rear blower only gets weaker and noisier, so changing the assembly put the back-of-the-car aircon back where it should be.