A friend of mine wrote me this:
I understand everything (what) you write.
I mentioned that it was probably better to write 'that' instead of 'what´. We were not able to find the correct answer, partly because it is not our mother tongue.
What can be used as a fused relative pronoun - the equivalent of "that which". So "I understand what you write" is grammatical and idiomatic.
You are trying to use it as a relative pronoun or subordinator, qualifying everything. This is common in some varieties of English, but not (as far as I know) in any standard varieties. So "I understand everything what you wrote" is not grammatical in standard English. (For a well-known example of this non-standard usage, see The Play What I Wrote, a play about comedy double acts. The title is a catch phrase that the duo Morcambe and Wise used in their show, which was deliberately non-standard for comic effect. )
So you need to follow "everything" with either a separate relative pronoun ("which") or a subordinator ("that") - or nothing, because where the relative pronoun is not the subject of the relative clause, you can omit it.
I would say these are in reverse order of naturalness, so the most natural form in speech is
I understand everything you write.
The next most common, and slightly more formal, is
I understand everything that you write.
The third possibility, while grammatical, is less usual:
I understand everything which you write.
(You may find people who say that you can't use "which" in a restrictive relative clause. They are wrong. Oliver Kamm says in Accidence Will Happen: "One thing you won't find in style guides that advocate the that/which rule is the slightest substantiation for it").