This one's trickier than it looks. We're used to hearing "who" in everyday conversation, but we're tempted to use "whom" when asked just because it sounds more formal and therefore, shouldn't that be correct?
Okay, in this case, your reflective instinct—only because you were asked—will give you the right answer, but that's not always going to be correct!
The correct answer here is "b) I don't know whom this report is for."
Let's deep-dive and figure out why, shall we? I don't want you to use "whom" everywhere that sounds formal and fancy and wind up using it wrong!
Quick and easy tip: Substitute "him" for "whom" and "he" for "who" and you'll get the right answer, though sometimes you'll need to re-arrange the words for it to make sense, since "who" statements are often questions. In the above example, we have to rearrange "whom this report is for" to "this report is for whom" or "this report is for him."
Classic quickie example: "For Whom the Bell Tolls" or in our rearrangement, "The Bell Tolls for Whom/Him"
An easy tip, if you remember prepositions [and if not, see Schoolhouse Rock for a fun refresher], "whom" is the object of a preposition, just like "him" is. "Who" is a verb's subject (doing the action) and "whom" is a verb's object (receiving the action). [Want a refresher on verbs? Schoolhouse Rock to the rescue again!]
Who will be attending? (subject of the verb "will be")
The report is for whom? (object of the preposition "for")
Whom is the report for? (it may be placed at the beginning of the sentence and look like a subject, but it's still the object of the preposition "for" and is a sneaky rearrangement of the previous example)
To whom do I address the letter? (object of the preposition "to")
It's clean-out day! Whoever left food in the break room refrigerator better grab it before it's thrown away. (subject of the verb "left")
Want a tip for that last example? When you're unsure about "whoever/whomever" usage, substitute "he who" or "him who" to help. "He who left food in the break room..." or "Him who left food in the break room..." Oh yeah, now I know which is correct!
PS You may be all a-tizzy about my quiz statements ending in a preposition. Honestly, there's no rule against ending prepositions. It's not recommended for formal use, but for the most part, you're allowed. Go for it.