Respuesta :
Actually it's pretty easy to distinguish a noun phrase from not a noun one. Everything you need to know whether the highlighted object is noun(also can be pronoun or rarely adjective), that's it. So, (the two squirrels) (to my sister) (my water) are parts of the noun sentences and (to go dancing) is expressed by action, so that is the answer.
Just took the test, answers:
The two squirrels are fighting over an acorn.
(Noun Phrase)
I gave half of my lunch to my sister yesterday.
(Not A Noun Phrase)
Maria loves all styles of dance.
(Noun Phrase) - Totally different choice on quiz -
I like ice cubes in my water.
(Noun Phrase)