。
She hates leaving anything unfinished.
Literal
She [topic-は] anything do-finish-not-without-で leave-alone [nominalizer-の] [subject-が] dislikes is.
A dense knot of negatives that yields a positive trait. 何事も in this affirmative-with-も frame means 'anything (and everything),' with the も extending universal scope. やり終えないで is V-ない + で = 'without finishing,' connecting to 放っておく ('leave alone, ignore, neglect'). Wrap the whole verbal phrase in nominalizer の and feed it to が嫌い ('dislike'), and the sum is 'she dislikes (the act of) leaving things unfinished and untouched.' The trait the sentence describes is what English would call 'thoroughness' or 'a need for closure.'