Is this a 2006 A4 or a 2007 A3???
What they’re telling you about the carbon is possible, but there are other things that can cause multiple misfires on multiple cylinders. Without the codes it’s tough to guess. Post them here when you get them and we’ll start there. NOTE: they should be listed on your copy of the shop order. You should always keep those. I don’t believe they’re trying to pull one over on you, but how well they did the diagnostics can only be guessed at without the codes.
As regards the cost… that’s the problem with owning an aging Audi. They’re great cars (my son has one, his second actually) but the cost of repairs is much higher than Toyotas or Hondas… or even VWs, with which they share some parts. VW owns Audi