wickedvikram
Farcry
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 .
But the phrase after comma could be referring either to Americas or to Maya
It is indeed a confusing concept as not much is available to test this scenario.
My simple guide is to remember that when
'WITH' is accompanied by noun/noun-phrase it gives extra information about the previous clause by stating information that relates to the subject of that clause.
Stating few more examples :
1) The dogs growled at the campers, with their fur standing on end.
2) Eighteen separate town camp communities are there today throughout Alice Springs, with 204 houses.
3) People rushed past me, with briefcases in hand.