The complete sentence is I'd do a nything to stop me having to deal with customers and their complaints! But it is commonly shortened to just say I'd do A nything to stop me having to deal with customers and their complaints! I'd do anything ( or sometimes I'd give anything) is just an idiomatic way of expressing frustration about something Here are more examples.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
The complete sentence is
I'd do anything to stop me having to deal with customers and their complaints!