The ancient Maya civilization was one of the most advanced in the Americas, with a sophisticated calendar system, a complex writing system, and impressive achievements in astronomy and mathematics.
(a) The ancient Maya civilization was one of the most advanced in the Americas
Correct. The phrase after comma ( with a ......mathematics) gives extra information about the independent clause preceding it- like what makes the Maya civilization advanced. We can identify such phrases by removing them completely and noting if the independent clause still makes sense . (b) One of the most advanced civilizations in the Americas were the ancient Maya
Wrong because plural verb 'were' is used for singular subject 'Maya civilization' .(c) Being one of the most advanced civilizations in the Americas, the ancient Maya
Wrong because 'being' is used incorrectly here. The Maya civilization is not 'being' anything.
(Being consistent with a study plan, Mark achieved a good score. - Correct since here Mark is being consistent. Hope this makes it clearer.)(d) The ancient Maya, one of the most advanced civilizations in the Americas
Wrong as it lacks a verb.(e) One of the most advanced in the Americas, the ancient Maya civilization
Wrong as it lacks a verb.