This means, " He was happy to see young people talking in just the way their parents had been told not to." Does that help?

It looks like the sentence you are quoting is using bad grammar. I think it should say this: "He said he was heartened to see younger generations learning to communicate in precisely the same manner in which their own parents were discouraged." In this sentence, "heartened" means 'made cheerful' or 'encouraged.' "Communicate in precisely the same manner" probably refers to whatever manner of communication his parents spoke in, but it is hard to say without context. I hope that helps!