@Jane and Aleh La: не нужно ни "what", ни "that".

Yes, THAT is needed . I can send you a picture with the proof. Tell me how.

Aleh, I got your email, thanks :)

No probs!

Excuse me for cutting in. To be honest, when there's a personal pronoun present, we don't use usually say THAT ( although it's correct ): anything you want, anything he says, anything we do. So I don't agree that THAT is needed, per se. For some reason modern English doesn't like THAT. For instance, you'll never hear someone say "I think that he's coming." In fact, it almost sounds awkward, too long. Everybody says "I think he's coming." So to answer your question, you're both correct, but Olga's version is more idiomatic.

In this case I'm going with Betty Schramper Azar - Undrstanding and Using English Grammar. It's not an old textbook.

...which, again, is perfectly correct.

Thank you, Uly, for an interesting info. I mean I don't think I've actually ever heard people saying "anything that you want". "That" is usually omitted wherever it's possible.

Absolutely. Like I said, it can sound downright unnatural.

Aleh, I don't mean to beat a dead horse, but I want you to have the best information possible. Please consider the following: https://books.google.com/ngrams/graph?content=anything+you+want%2C+anything+that+you+want&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Canything%20you%20want%3B%2Cc0%3B.t1%3B%2Canything%20that%20you%20want%3B%2Cc0

I got your point. ) I'll talk to you later.

Ок