What is the difference between these two phrases?
worst way possible
worst possible way
The "worst possible way" describes the intensity of the desire.
The "worst way possible" describes the undesirability of the 'way'. For example:
"He wants chocolate ice cream in the worst possible way." (He really, really, wants chocolate ice cream.)
"He wants chocolate ice cream in the worst way possible." (He may want a chocolate ice cream enema - you probably don't want to stick around to find out.)
"She has done it in the worst (possible) way (possible).
@user129054 - In your comment under the question, you give the above sentence as context (note I have added the definite article). In that case I would use:
"She has done it in the worst possible way."
Either version is grammatically correct. However my reason is that, to my ear, it sounds better. I emphasise "to my ear" because it is a matter of the rhythm of the sentence. I don't know how to show musical notation here so I can't demonstrate it that way. I can only say that 'possible' consists of three rapid syllables with emphasis on the first.
Perhaps it is the musician in me but it sounds better rhythmically as "worst possible way".
Note: I expect some criticism for this answer but that's the way I feel.