Answer:
The detective said, “If you see or hear anything, please don’t hesitate to call me.”
Fourth choice
Explanations for each sentence:
I think my Aunt should consider calling ahead to see if we can get a reservation.
"Aunt" doesn't need to be capitalized because it's not a proper noun. For example, "aunt" needs capitalization if you said: I think Aunt Lisa....... because "Aunt Lisa" is a proper noun.
My High School has been taking a field trip to a farm outside of Iowa City for years.
"High School" doesn't need to be capitalized because it doesn't have the specific name of a high school.
I asked my neighbor if She would pick up my mail while I am out of town.
"She" doesn't need to be capitalized. Pronouns (which replace a noun) don't need to be capitalized unless the pronoun is "I".
The detective said, “If you see or hear anything, please don’t hesitate to call me."
The correct capitalization is used here. The tricky words might be "detective", which is lowercase because there is no specific detective name. The word "If" is capitalized because it's the first word in the quotation.
