Answer:
A. I might allow her in if she behaved.
Step-by-step explanation:
This is a phrase that is conditional in mood because the speaker's letting her in is contingent upon (depends on) her behavior. It also uses the word "might". Whenever you see the words "might" or "would", think conditional (I know this well from taking French class).
B is not a conditional phrase because there is no "might", and C is not a conditional phrase for the same reason. D might seem at first glance to be a conditional phrase, but it is more-so hypothetical and does not depend on anything.