Learn French: Nous ne préparons aucunement une acquisition hostile. - We are not in the least preparing a hostile acquisition.

Ne... aucunement is an emphatic absolute negation. While Nous ne préparons pas simply means "We are not preparing", replacing pas with aucunement translates to "not in the least" or "not at all". It is a much stronger, more formal denial.

Where exactly does aucunement go in a sentence?

Because aucunement is an adverb, it takes the exact same spot that pas would. Here, it goes directly after the conjugated verb préparons. If this were in a compound tense like the passé composé, it would go between the helping verb and the past participle (for example, Nous n'avons aucunement préparé).

Shouldn't une change to d' after a negative verb? Why isn't it aucunement d'acquisition?

You learned earlier that indefinite articles (un, une, des) usually change to de or d' in negative sentences. However, you can keep un or une when there is an implied contrast. By saying une acquisition hostile, the speaker stresses that they aren't preparing that specific thing, but perhaps something else (like a friendly merger).

Could I use nullement instead of aucunement here?