I just bought two new front tires for my Audi A8 with Quattro all-wheel drive and was told I should replace the back tires as well. I can't afford those tires for a week or so. How long can I drive the car with old tires on the rear before it starts to ruin my differential?
If you call different Audi dealers you're likely to get differing answers regarding how much tread depth difference is OK for the all-wheel-drive system. Nonetheless, I would advocate calling to get specific recommendations for your vehicle, as some all-wheel drive systems are more sensitive to differences in tire size than others.
I would add, however that if you choose to stick with only two new tires, and if the tires you're not replacing have significantly less tread, the current "safety-minded" recommendation is often to put the new tires on the rear (not the front, as you have indicated). The thinking is that if you have new tires on the front and old tires at the rear that the car may be inclined to oversteer (i.e. go into a spin, "hang the tail out"), which is potentially more dangerous than if you had less grip at the front.
Your drivers handbook will carry Audi recommendations for your tyre fitment. With an A8 it is to have matching tyres on an axle. Tyre shops will suggest it is a good idea to have a complete set in any event. (All the major chains in the UK pay their staff where the more sales they make, the more money they are paid. One of the reasons why they are held in such disregard.) The adoption of fitting new tyres to the rear came about from the fact that the new tyre has a coating on it to release the tyre from its mould during manufacture. The reasoning was that if you drove 200 miles with new tyres on the rear, not only is the coating removed but the tyre is 'proven to be good'. The front tyres do the real work when it comes to steering, braking and load carrying and should be the best. The big thing about tread depths, when compared front to rear, came about when the Vauxhall Frontera from some years ago was destroying transmissions because of trans windup with tyres differing by about 3mm. It does not happen today. Especially with a VAG vehicle.
I drive Landrover. Had my front tyres changed today and driven approx 6 miles and differential had enough and playing up. Disappointed that garage didn’t even mention that it’s beter to have rear tyres changed for 4wd first. Now it’s going to cost me atleast £1k to have it fixed. Follow the advice, rear tyres should always be better than front tyres.