Theory:

     He said, “It looks to me as if the bearings were all wrong.”
 
     I said, “Don’t you trouble about it any more; you will make yourself tired. Let us put it back and get off.”
 
     He said, “We may as well see what is the matter with it, now it is out.” He talked as though it had dropped out by accident.
 
     Before I could stop him he had unscrewed something somewhere, and out rolled all over the path some dozen or so little balls.
 
     "Catch ‘em!” he shouted; “catch ‘em! We mustn’t lose any of them.” He was quite excited about them.
 
     We grovelled round for half an hour, and found sixteen. He said he hoped we had got them all, because, if not, it would make a serious difference to the machine. I put them for safety in my hat. It was not a sensible thing to do, I admit.
Explanation:
 
The narrator was worried about his bicycle. But he was a meek person, and hence he tried to dissuade the man gently. He asked the man not to trouble himself with the cycle any more because he would become tired. The narrator suggested that they should put it back and start their journey.

The man, on the other hand, thought that they should delve more into the problem, and proceeded with unfastening more screws and bearings. All of a sudden, several balls came undone and rolled all over the path. Then, the men crawled on fours and started looking for them. After spending about half an hour, they were able to find about sixteen.

The man hoped that they found all the missing balls, as he believed that it might cause a big difference with the machine. Of course, the humour is hard to miss in this sentence. We see the man talking about the serious difference the missing balls would cause when, in reality, he had effortlessly dissected the bicycle into pieces. What more can the little balls do that the man hasn't done himself?

Listening to the man's warning, the narrator did something extremely ridiculous with the balls. He put them in his hat for safety, fearing that he might lose them.
 
ball-bearings-1958083_640.jpg
Ball bearings
 
Meanings of difficult words from the paragraphs:
 
Sl. No.
Words
Meanings
1
BearingsA part of a machine that allows one part to rotate or move in contact with another part with as little friction as possible
2
GrovelledLie or crawl abjectly on the ground with one's face downwards
3
SensibleDone or chosen in accordance with wisdom
Reference:
National Council of Educational Research and Training (2007). Honeycomb. A Bicycle in Good Repair (pp. 126-132). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.