First of all, it is important to define adjective phrase in order to find our answer. It is a group of words that describe a noun or a pronoun. So option A (curly-haired Bob played a game because the "curly- haired" is an adjective phrase that modifies the noun Bob. The other possibilities do not show a group of words with adjectival reference that might define a noun or pronoun.
I believe that “to keep alive” is the correct answer based upon the context.
It was the Iranian hostage crisis.
Katniss and Rue remain up to steal there food/supplies. Rue will set a fire to distract the careers while Katniss was to go destroy the supplies. but upon her staking out the items while the careers run to the fire source, Katniss realizes there are land mines placed around the supplies, so she shoots a bag of apples with an arrow and watches the fiery explosions from the impact of the mines.