This exercise is easier than you think. Fend off is transitive verb, so it has to have an object. You fend off something or someone. Fight back is an intransitive verb, so it has no object. So you have to use 'fend off' in the first sentence, because there's an object - "At least I know how to fend off an attacker" - and you have to use fight back in the second sentence because there is no object - "I know how to fight back". Simple, isn't it?

Yes, this can be very confusing! "Fend off" is usually in a situation where you are in a fight, but you want to get away. You have to defend yourself, but in the end you're doing everything you can to stop the fight or to get away. "Fight back" means that you're actually attacking the person or thing that is attacking you. So when you're fending someone off it CAN involve fighting back because you might want to scratch their eyes or kick them in the... well... painful areas. It depends on the situation, but fending off is more for "defense" and fighting back is more for "attack". Did that help?

Fend off is more passive. It means you are protecting yourself from someone else's attack. Fight back is active. You are actively going out and fighting back against something or someone. You would only fend someone off if you absolutely had to. You can choose to fight back if you are angry about the way someone is treating you, or if you want to stand up against injustice. In the answer, you'd want to switch the two terms. A: Today's training has really zeroed me out! At least now I know how to 【fend off 】(protect myself from) any attacker. B: Yes, it's hard, but it's good to know how to 【fight back 】(attack instead of being the victim) if you are in danger. Does this help?

It might help to realise that "fend off" has, as its core meaning, "push away" or perhaps "use force to repel". For example, when you are in a small boat approaching a dock, you might want to avoid hitting it, so you would push away with your hands. You might yell "fend off" to tell people in the boat to do that. "Fend off" is also used figuratively. For example, to "fend off awkward questions" would be (in some way) to deter or push away questions you did not want answering. In a situation of attack, "fending off" focuses on the pushing away of the attackers, by some means, whereas fighting back could include many actions some of them more active - as George says, it is a more active thing to do.