"Can the answer you impart" is grammatical but it does not follow normal syntactical rules. It would be correct to say: "Can you impart the answer?" In English, you invert a sentence to make it a question, by pulling the verb out - usually the helping (auxiliary) verb* - and putting it at the beginning. In this case the sentence, before it's inverted, is "You can impart the answer." When you invert it, you pull out the helping verb "can" and take it to the beginning: "Can you impart the answer?" However, "Can the answer you impart?" can also work as a sentence, just not a normal one; you're really only likely to find it in poetry, where you can rearrange things in different ways to fit your words to your chosen syllable patterns. In this case, the person writing the sentence has, first (before inverting the statement into a question), switched the word order of the original statement to "The answer you can impart." This just means "You can impart the answer," but the person put "the answer" at the beginning. You can do that - you can put the object of a sentence at the beginning - but it doesn't happen in normal speech, so if you do it in poetry, it usually means you're desperate to get the right words into the rhythm you want, and can't come up with any other way to do it. So it's sometimes frowned upon. Anyhow, after rearranging it that way, they inverted it as you would invert any question: by taking the main verb to the beginning - "Can the answer you impart?"
Another example of this poetical rearrangement of words can be found in "The Raven": "Not the least obeisance made he; not a minute stopped or stayed he..." In more normal-people language, this means "He made not the least obeisance [courtesy]; he stopped or stayed not a minute...". Also, Yoda did this sort of thing all the time.
*Even if there isn't an auxiliary verb in the original sentence, in English you still pull one out - you just have to add one first. So, "They shoot canoes" becomes "They do shoot canoes" becomes "Do they shoot canoes?". This is tricky for people learning English from other languages.
Technically, it is correct because it has a subject and a verb. However, its syntax can be improved to sound better - 'Can you please know?'
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