A lot of people are trying to explain 就 vs 才 with english equivalent terms, but that makes it very confusing when it can be explained with simple logic statements, and it is crucial to understand the reasoning behind all these cases:
下雨的話地就會濕下雨的話(X)地就會濕(Y)
The floor getswill get wet (Y) [if] it rains (X)
下雨的話地才會濕下雨的話(X)地才會濕(Y)
The floor getswill get wet (Y) [if and only] if it rains (X)
你怎么想我就不在乎呢。你怎么想我(X)就不在乎呢(Y)。
I wouldn't care (Y) [if] however you think of me (X)
你怎么想我才不在乎呢。你怎么想我(X)才不在乎呢(Y)。
I wouldn't care (Y) [if and only if] however you think of me (X)
You see, "I wouldn't care" is the result of "however you think of me", the action. By using 就 you are simply stating that you wouldn't care how he thinks of you. But in some cases that's not powerful enough, and only in chinese that you can deliver that kind of tone. You: you want to tell the other person you don't care so much that "however you think of me" is the ONLY thing that you don't care about, and you care about everything else.
两个人就能办好。两个人(X)就能办好(Y)。
It can be done (Y) [with] two people (X).
两个人(Doesn't tell you anything about completing with 1 person or 3X)
两个人才能办好。才能办好(Y)。
It can be done (Y) [with and only with] two people (X).
那就是菲尔普斯,又贏獎牌了那就是菲尔普斯(Y),又贏獎牌了(X)
That is Michael Phelps (Y), winning yet another medal (X)