Should I say:
- I've made a huge mistake by accepting this offer
- I've made a huge mistake in accepting this offer
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Should I say:
I have made a huge mistake by accepting this offer.
I have made a huge mistake in accepting this offer.
I think there's no difference in meaning between these sentences.
You usually use the structure mistake + in + -ing form. Even you can drop the preposition 'in' that's optional.
I have made a huge mistake accepting this offer.
It'll also be grammatical if you say:
I made the huge mistake of accepting this offer.
As for the use of the preposition "by", though not as common as in, it's also correct in the sentence; we use it for stating the way we do something.
Both of these choices are perfectly correct. It is immaterial whether you choose by or in here, since the meaning really does change depending on your choice.
I suppose you could argue that the first choice "by" has a nuanced and very slight implication of a more passive acceptance, and the "in" has a nuanced and very slight implication of a more active acceptance, but, that arguement is really splitting hairs.
The choice between by and in here is entirely a personal choice based on the sound of the sentence, and not its meaning. I hear both usages on a regular basis in my everyday life.