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Is it "John and Becky's knowledge" or "John's and Becky's knowledge"?
If you want to communicate that John and Becky both possess the same knowledge (i.e., you're referring to the idea that they both possess knowledge about English grammar), then you'd add an apostrophe onto just the last person listed (e.g., John and Becky's knowledge).
If you want to communicate that John and Becky possess different knowledge (i.e., you're referring to the ideas that John possesses knowledge about English grammar and Becky possesses knowledge about Hungarian grammar), then you'd add an apostrophe onto both John and Becky (i.e., John's and Becky's knowledge).
See the section titled "Joint and separate possession" at http://en.wikipedia.org/wiki/Apostrophe
Does the knowledge below jointly to John and Becky as a single entity, or to them both individually? Is it John's knowledge and and also Becky's knowledge, is it is the knowledge of John and Becky as a couple? That will determine whether you have two possessives or a joint possessive. In either case, it might be better to reword the expression, e.g. "the knowledge of John and Betty" or "the knowledge of both John and Betty".