来週までに漢字を30字おぼえておかない といけない。[覚える]
By next week, I have to memorize 30 kanji in advance .
I don’t get why the correct answer is what it is. Is that a negation at the end? How did that get in there?
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I believe that is just another variation of なければいけない for ないといけない which emphasizes the “have to” while “ておく” is the “in advance”.
The blue and red dictionary grammar books make mention in the index but not on any page from what I can see about ないといけない. Couldn’t find in in the white grammar “handbook” either.
Seems like a there are a million ways to say “should” but sounds like a useful grammar point if wanted to keep your friends/family alive in Edo period Japan or unless suffer severe consequences 
. Might as well have few creative ways to express it 
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@Nenad
Like @s1212z said, this is another way to say “must/have to”.
Verb[ない] + といけない（ならない）
@s1212z
Living in that period was hard 
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Almost all of Japanese’s expressions for “should” or “must” involve double negatives.
In fact, even ending a sentence with なきゃ (slang, short for なくては) is enough to imply なくてはいけない or なくてはならない。Ending a sentence with ～ないと is also interpreted the same way, as in “it won’t be good if ◯ isn’t done,” which is effectively “have to ◯” or “should ◯.”
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It’s funny, because double negatives in English are usually discouraged as either sloppy or less coherent for speaking/writing. When I hear them, I will do a double-take just be certain on the understanding as I don’t find it pleasing to hear for its indirectness. For Japanese of course, there is this undertone of indirectness that is used all the time in grammar as well as intent so it works well in that aspect.
Just as an experiment, I gave English double negative examples to my Japanese friends and without any hesitation they understood the meaning and found it very comfortable to use 
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