In this exercise:
Ali stopped _____ to his friend. He talked to him then.
a) talk
b) talking (I chose this one)
c) to talk (This one is marked as the correct answer)
d) being talked
Why did they choose "to talk" as the right answer? And why not "talking"?
I understand the meanings of talk and stop so I don't understand why one is wrong and the other correct.
Infinitives of purpose
We can use an infinitive of purpose at the end of a clause to explain WHY we do something or did something:
In the sentences above, why did I come to London? To learn English! Why did I go to the shops? To buy some milk! Why am I studying hard? To go to university! Notice that the infinitives of purpose here have no special relationship with the verb. They are Adjuncts. They give us extra information about the sentence and explain why someone did something.
Stop + --ing:
The verb stop can take an -ing clause as a Complement:
The -ing phrases above explain what action finished. So I finished smoking and running and reading my book. Sometimes we don't need to use an ing clause to explain what stopped, because the listener can already understand this:
In the second sentence above we understand that it stopped raining. We don't have to use the verb raining a second time. Or consider this sentence:
In the sentence above, we understand something like stopped going home, or stopped walking or stopped driving. The exact action is not very important.
Using both things together:
So we can use a sentence with the verb stop with or without an -ing clause afterwards. Whether or not we use an -ing clause, we can also use an infinitive of purpose to explain why we stopped (doing something). So I can say:
In the sentences above, if the listener knows I was already smoking or eating I could leave the -ing clause out:
Notice that the infinitives of purpose have no special relationship with the verb stop!!! They are just extra bits of information.
The Original Poster's Question:
I have added the word right to make the second sentence more natural. Now if Ali stopped talking, it means that the talking finished. But this is not possible because Ali talked to his friend! But if Ali stopped (doing something else) because he wanted to talk to his friend, then the two sentences make sense, because Ali did talk to his friend. This is why the infinitive of purpose to talk to his friend is the best answer.
Stopped talking
Ali was talking, but then stopped talking and did something else.
Stopped to talk
Ali was doing something (like walking), but then he stopped that something and started talking.
Stopped talking:
Ali was talking to his friend. When they finished, he stopped talking to his friend and went to the store.
Stopped to talk:
Ali was walking down the road. He saw his friend, and stopped to talk with him.
For the above picture, added by OP, per OP's comment:
I'll be revising all my lessons.
That is fine. That means that you will revise your lessons for an undetermined time frame.
I'll have revised all my lessons by next Friday.
That is the intended correct answer. That means that by next Friday, you will have the lessons completely revised.
I'll be revising all my lessons by next Friday.
That just sounds wrong, to my ears. It means that you will continuously be revising your lessons, but it wants an "until." A "by" afterward sounds wrong.
I'll be revising all my lessons until next Friday.
That also sounds right, but has a slightly different meaning. It means that from now until Friday, all you will be doing is revising your lessons.
to talkwould be appropriate, implying that Ali was on his way somewhere else. if him is somebody else, say, a customer, thentalkingis appropriate, implying that Ali started to address somebody new.