The brief
The A4 had reddish-brown fluid pooling under it, around the transmission, and the gearbox had started slipping, with harsh, erratic shifting and the odd whine. He brought it in. Reddish-brown fluid near the transmission is automatic transmission fluid, the ATF, and a leak there usually traces to the pan gasket that seals the bottom of the box. The ATF lubricates and cools the gears and clutches and carries the hydraulic pressure that shifts them, so when the gasket weeps and the level drops, the box runs low: it slips because there isn't enough pressure to hold the clutches, it shifts harshly, and the lack of lubrication makes it whine. A leak that drops the level is one you fix before the box wears.
The diagnosis
On the lift the leak traced to the transmission pan gasket, weeping along the seam, with the rest of the transmission housing dry. The fluid level was low from the leak, and the fluid that was in there was darker than it should be, so it was getting a full change while the pan was off. So the call was a pan gasket replacement plus a fluid and filter change, drop the pan, new gasket, new filter, fresh ATF to the correct spec and level, rather than just topping it up onto a leak.
The work
The transmission pan was dropped, the old fluid drained, and the old gasket and filter removed. The pan and the magnets were cleaned, a new genuine Audi-spec pan gasket and filter fitted, the pan torqued back up, and the box refilled with the correct ATF to the proper level following the fill procedure, with the fluid temperature checked so the level was set right. A road test followed to confirm the slipping and the harsh shifts were gone and there was nothing dripping.
The outcome
Smooth, prompt shifts, no slipping, no fluid under the car, and the level holding. The A4 went home with the transmission back to spec. A leaking pan gasket drops the level and a box run low wears its clutches, so resealing it and doing the fluid and filter rather than topping it up protected the box and put the shifting right.