Select noun phrase if the underlined group of words is a noun phrase. select not a noun phrase if the underlined group of words is not a noun phrase. (choices in attachment)

"the price for an item is too high" - not a noun phrase. Actually, this is a clause, as it has a predicate of its own.
"a bottle of water while strolling" - not a noun phrase. "A bottle of water" would be a noun phrase (a phrase that has a noun as a headword), but "while strolling" is an adverbial phrase that describes the verb "buy".
"The same brand of bottled water" - noun phrase. The headword is "brand", and all the other words cling to it and provide additional explanation.
"a pair of athletic shoes" - noun phrase. The headword is "pair".

Aslender threadlike object or fiber, especially one found in animal or plant structures.