Which words in the sentence make up the infinitive phrase?
before the show, they went to find the water fountain.
a. to find the water fountain
b. before the show
c. to find
d. went to

You can find the infinitive phrase by placing 'to' in font of each of the words. My teacher taught me this. Whichever statements make sense are the infinitive phrases.
So lets begin:
To before
To the 
To show (show the noun; like event, so 'to event')
To they 
To went 
To to
To find
To the
To water (again the noun; like liquid)
To fountain
Of course the only phrase that makes sense is 'to find', so I believe the statement beginning with 'to find' is the correct answer.
'to find the water show'
Sorry this was long, but hope it helps anyways :)

Googly eyed because it sounds like a silly thing to call someone