While 5-year-old hope was looking at one of the balloons her mother set out for her birthday, her brother took a pin and popped the balloon, causing hope to flinch and blink. later during the party, when her mother approached her with a balloon, hope blinked and flinched. this is an example of conditioning?

This might be an example of classical conditioning. After her father popped the balloon causing her to flinch and blink when them other brought a balloon she might associate it with her previous experience. This conditioning makes reference to a learnt procedure in which a biological stimulus is paired with a neutral stimulus. 

Ithink the answer you are looking for is (b).