Which of the following correctly punctuates an essential expression? architecture, so popular with native americans, is still a flourishing art. mexico city is home to several museums that display the country’s past. the national historical museum, which is in chapultepec castle, is concerned with mexico’s history since the spanish conquest. mexico, where sports are popular, has hosted the olympic games and the world cup. description

The two examples which correctly punctuate an essential expression or element in the sentence are:

Architecture, so popular with Native Americans, is still a flourishing art.

Mexico, where sports are popular, has hosted the Olympic Games at the World Cup.

Some constituents that alter a sentence are indispensable and restrict the meaning of an altered word or prhase, whereas others aren't indispensable and don't affect its meaning. The first ones are separated from the main idea using commas.

Mexico City is home to several museums that display the country’s past. Here we don't have any non essential element.

The National Historical Museum, which is in Chapultepec Castle, is concerned with Mexico’s history since the Spanish conquest. Here, information can't be ommited and in fact, shouldn't be set off with comas, since such expression contains essential information (it is not any National Historic Museum but the National Historic Museum which is in Chapultepec Castle).

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it was surely an odd creature that one made up by reading the historians first and the poets afterwards a worm winged like an eagle; the spirit of life and elegance and charm,   in a kitchen chopping up suet. but these creatures, monst'r however entertaining to the imagination, hast no existence in fact. what one might doth to bringeth h'r to life wast to bethink poetically and prosaically at one and the same moment,   thus keeping in toucheth with fact—that the lady is mrs martin, ag'd thirty-six, did dress in blue, wearing a black coxcomb and brown shoeth; but not losing sight of fiction eith'r—that the lady is a vessel in which all s'rts of spirits and f'rces art coursing and flashing p'rpetually. the moment, howev'r, yond one tries this method with the elizabethan mistress, one brancheth of illumination fails; one is did hold up by the scarcity of facts.   one knoweth nothing detailed, nothing p'rfectly true and substantial about h'r.   hist'ry scarcely mentions h'r.   and i did turn to professeth'r trevelyan again to seeth what hist'ry meanteth to that gent.   i hath found by looking at his chapt'r headings yond t meanteth.