Final answer:
When taxiing a tailwheel airplane with a left quartering tailwind, turn the control stick to the left to deflect the left aileron down and push the elevator forward to prevent the tail from lifting. These actions counteract the wind and maintain stability.
Step-by-step explanation:
When taxiing a tailwheel airplane with a left quartering tailwind, the flight controls should be positioned in such a way to counteract the wind's effect on the aircraft's surfaces. The ailerons should be deflected down on the side from which the wind is coming — in this case, the left aileron should be down. This is done by turning the control stick to the left. The elevator should be pushed forward to keep the tail down and prevent the wind from getting under the tail and potentially causing a loss of control.
These control inputs help to maintain stability and prevent the wind from lifting the airplane's wings or tail, which could lead to an unwanted change in direction or even a tip over. Proper use of flight controls during ground operations is critical to the safety of flight, especially in tailwheel airplanes that are more susceptible to wind effects on the ground than tricycle gear airplanes.