Let's start from the second blank. We are told simple math wouldn't suffice, so the word we're looking for here must be something like "advanced" or "complex."
Now that we know that some advanced techniques were needed, we can say that without them, calculations in Mayan calendar would have been "difficult" - and that's the kind of word we need for the first blank.
Of the answer choices, only choice (A) has a word that can be used to describe difficulties: "onerous." "Onerous" means "burdensome," and it fits the first blank perfectly. Looking at the second word in choice (A), we can see it's appropriate for the second blank—it's "adroit," which means "clever" or "skillful." The only other answer that could seem to fit the blanks is choice (E), since "unpredictable" signalizes some difficulty. However, we don't usually say that calculations are unpredictable, so it would sound rather awkward. Also, "improvised" doesn't imply any level of complexity, so it doesn't really fit.
The correct answer is (A).