Explain the significance of Sonny's & Homer's conversation after Ike Bykovski teaches the boys how to weld in October Sky.
The conversation that occurs between Sonny and his Dad after Bykovski helps him with his rockets serves to foreshadow disaster for Mr. Bykovski, and also galvanizes Sonny to continue with his experiments in defiance of his Dad's direct orders.
When Sonny asks Mr. Bykovski to teach him to weld, the old man says that it would be quicker this time if he just did it for him; he says he will teach the boys to weld another time. Bykovski makes the boys three rockets, and when the boys set them off, one of them flies wildly and "takes a chunk out of the brick wall of (Sonny's) Dad's office." In effect, "the BCMA had rocket-attached the coal company, and Sonny's Dad is furious. Realizing that the rocket is made with company materials, Sonny's Dad says his son is a thief, and so is the man who helped him build the rocket (Chapter 6).
The exchange that occurs between Sonny and his Dad immediately thereafter is more of a lecture than a conversation. Sonny's Dad forbids him to fly any more rockets, and asks who helped him make the ones he set off already. When Sonny does not answer, his Dad concludes that it's "got to be...Bykovski," and vows to "take care of him." This threat foreshadows that something bad will happen to Bykovski, and Sonny's Dad does in fact make good on his promise by taking Bykovski out of the welding shop and forcing him to work again in the mine. Although Bykovski's new position pays more money, it is much more dangerous, and the Bykovskis are torn in their reaction to Mr. Bykovski's new position. Bykovski eventually is killed as a result of an accident at his new job, but before he dies, he remains loyal to Sonny; instead of being angry at him, he encourages him to continue with his research in rocket science.
As a result of his conversation with his father, Sonny realizes that his father is unequivocably against his interest in rockets. Sonny resolves to continue in his work with the rocket boys despite his father's explicit directions to desist in his activities. Having been branded an outlaw, Sonny is all the more determined to succeed in his efforts to unlock the secret of rocket science (Chapter 7).