What problem did the separatists see how did they propose to solve it?

I guess the question is referring to the problem when the Puritan "Separatists" reached the Massachusetts Bay in 1620, they did not posses any rights by law nor did they have any kind of established government etc.

They solved this problem with a compact called "Mayflower Compact", which proposed that people can follow a kind of government for the time being. The law will be the law of majority and it was a type of self-government.