"This is important for her."
取って means as for (blank). You have to put a に before it to signal that its for in this case, her.
It makes sense actually, because "totte" always goes together with "ni" when used like this; it means "as far as ... is concerned" or "according to". Compared to just using "ni" it emphasizes the fact we're talking about somebody's point of view.
I typed this with the kanji and was marked wrong. I've reported it (10/30/17).
EDIT: I think it's accepted now (2/22/18).
とって is quite confusing and i don't know what it means at this juncture. I know とても as very, which would make sense, but not とって
My answer (which was marked correct) was かのじょにとってこれはたいせつです.
Can anyone tell me if there is a difference or emphasis shift if I reorder the words like this?
As far as I can tell the difference seems to be "she regards this as important" verses "this is (the topic) she regards as important" but my Japanese isn't great.
Would any answer with 大事 (daiji) Be wrong? Is the neuance of "important" different? What would a valid answer (with 大事) look like?
They sound close but they mean different things. とても is an adjective, "very". とって, on the other hand, is more like a particle in terms of its function. It means "to" or "for", as in "this thing is very important to me".