I said, “It doesn’t if you don’t wobble it.” It didn’t wobble, as a matter of fact—nothing worth calling a wobble.
     He said, “This is dangerous; have you got a hammer?” I ought to have been firm, but I thought that perhaps he really did know something about the business. I went to the tool shed to see what I could find. When I came back he was sitting on the ground with the front wheel between his legs. He was playing with it, twiddling it round between his fingers; the remnant of the machine was lying on the gravel path beside him.
The narrator was obviously unhappy with the man's behaviour. He defended his bicycle by saying that it was perfectly healthy. He said that the wheel was shaking only because the man kept shaking it. But the man was prepared to ignore the narrator's feeble protests. He said that it is dangerous to ride a bicycle that wobbles and asked the narrator if he has got a hammer with him. The man was determined to fix the issue.
The man asked for a hammer

Although the narrator was worried about his bicycle, he thought that the man knew what he was doing. Hence, he decided to bring the man the tools he needed from his tool shed.
Tool shed
When the narrator came back with the tools, he was shocked to find the cycle in pieces. The man was sitting on the ground playing with the front wheel. It was held between his legs. The rest of the bicycle was lying on the path.
The front wheel was pulled out from the cycle
Meanings of difficult words from the paragraphs:
Sl. No.
Tool shedAn outbuilding for storing tools
TwiddlingTo twist, move, or fiddle with something
RemnantA part or quantity that is left after the greater part has been used, removed, or destroyed
A loose aggregation of small water-worn or pounded stones
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.