Theory:

Narrator: The tiger’s roar filled the cave with thunder. Mother Wolf shook herself clear of the cubs and sprang forward, her eyes, like two green moons in the darkness, facing the blazing eyes of Shere Khan.

Mother Wolf: And it is I, Raksha, ‘The Demon’, who answers. The Man’s cub is mine. He shall live to run with the Pack and to hunt with the Pack; and in the end, he shall hunt you!

Narrator: Father Wolf looked on amazed. He had almost forgotten the days when he won Mother Wolf in a fair fight from five other wolves, when she ran in the Pack and was not called 'The Demon' for compliment’s sake. Shere Khan might have faced Father Wolf, but he could not stand up against Mother Wolf, for he knew that where he was she had all the advantage of the ground, and would fight to the death. So backed out of the cave mouth growling, and when he was clear he shouted.

Shere Khan: Each dog barks in his own yard! We will see what the Pack will say to this fostering of man-cubs. The man-cub is mine and will come to me in the end!
Explanation:
 
The tiger roared in anger, and it sounded as if there was a huge thunder.
 
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Tiger's growl sounded like a thunder
 
For the first time since the appearance of the tiger, Mother Wolf jumped into action. She left her cubs aside and sprang forward. Her eyes were like two green moons in the darkness, and she glared at the burning eyes of Shere Khan.
 
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Mother Wolf 's eyes looked like a pair of green moons

We had seen previously how the tiger spoke in arrogance when he said, 'it is I, Shere Khan!', as if he was the supreme of all beings. Mother Wolf answered back in a tone that was equally mighty. She said, "and it is I, Raksha, ‘The Demon’, who answers."

Raksha is the name of Mother Wolf. In the Indian context, the word 'raksha' can have two different meanings. As mentioned by Mother Wolf, Raksha can mean 'the demon' as in the word 'raakshasee'. However, it can also mean 'protection'. Hence, the name identifies the two elements in her. She can be a demon to her enemies and a defence to her loved ones.

Mother Wolf continued her speech. She declared that the Man's cub belonged to her. Like her own little ones, the Man's cub would grow, live, and hunt with the Pack of wolves. She was so furious that she announced to the tiger that the child would hunt down and kill Shere Khan in the end.
 
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Mother Wolf declares that Man's cub would  grow, live, and hunt with the Pack

One could see how protective she has grown towards the Man's cub, and she was ready to fight the ferocious tiger.

Father Wolf, on the other hand, stood amazed, witnessing the might of Raksha. She used to be a strong wolf and would run and hunt with a Pack. The narrator says that the father had almost forgotten how wild the mother used to be in the past. Moreover, he had won her in a fair fight from five other wolves. She also had the nickname "The Demon" to symbolise the savage nature of her hunting. The name was not merely a compliment; she was almost like a demon.

Shere Khan didn't expect Mother Wolf to stand up against him. He backed off a little. Though the tiger had faced Father Wolf, he knew the fight with Mother Wolf would be different. Nobody can mess with an angry mother, for a mother may put everything aside for the safety of her children, and he could see that Raksha was ready to fight to the death. Also, given that he was too big to enter the cave, he knew he had a disadvantage and was at risk.

Hence, Shere Khan pulled himself out of the cave growling. When he knew he was clear and was no longer inside the cave, he shouted. He said how dogs might show their courage when they are inside their territory, meaning that they would become fearful elsewhere.
 
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Shere Khan backed off with a growl

As Father Wolf had said before, the wolves take order from the Chief of the Pack. Hence, Shere Khan reminded the wolves that they have a Pack and retorted how the Pack and their Chief might react to the rearing of a Man's cub. He left the cave by warning the wolves that he would get his hands on the Man's cub as the latter belonged only to him.
 
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Shere Khan can be seen leaving the cave
 
Meanings of difficult words:
 
S.No
Words
Meanings
1
Roar To make a long, loud, deep sound
2
Shook herself clear ofFreed herself from
3
Blazing To burn brightly and strongly (here due to anger)
4
DemonSomeone who is devilish, strong, and dangerous
5
Fair A respectful, structured way of confronting each other; a fight that is done according to the rules
6
Fight to the deathRefers to a situation where one is willing do anything to achieve or protect something, even if they suffer as a consequence
7
Backed out To withdraw from an agreement, etc
8
GrowlingTo make a low noise usually because one is angry
9
YardA piece of land
10
Fostering To take care of a child as if it were your own
Reference:
State Council of Educational Research and Training (2019). Term-3 English Standard-6. The Jungle Book. (pp 116 - 121). Published by the Tamil Nadu Textbook and Educational Services Corporation.