I will highlight all the prepositional phrases in the text: A prepositional phrase is a phrase that includes a preposition: a word that describes the relationship between things.
(1) Brenda would have liked to have taken her vacation at the beach.
(2)
However, the weather forecast on the television called for rain.
(3)
Also, her
fiancé, Max, wanted to vacation in the mountains.
(4) After a heated
discussion, Brenda and Max decided to compromise.
(5) They would spend
their vacation time at Spring Lake.
(6) That way, Jack could fish and
Brenda could enjoy swimming.
So we see that the one that does NOT have a prepositional phrase is the last one, sentence 6! The correct option is c.