When do you remove the ending a of greek prefix?

You remove the final "-a" from a Greek prefix when it's followed by a word or root beginning with a vowel. This is done to avoid the awkward juxtaposition of two vowels. It's a form of elision or crasis.

For example:

* An- +archy becomes anarchy. The "a" in "an-" is dropped before the "a" in "archy."

* A- +symmetrical becomes asymmetrical. The "a" in "a-" is dropped before the "s" (which is a consonant sound). Note that although the next letter is a consonant, it is often useful to consider the *sound* it begins with to avoid double vowels. If the next sound was a vowel, then you would drop the 'a'.

The prefix "ana-" is an exception; it generally retains its final "a" even before a vowel.

It's important to note that this is a convention of English spelling and word formation, not an inherent rule of Greek grammar. The original Greek forms often didn't involve this elision in the same way.