In the Second Treatise, how did Locke come to the conclusion that men are

equal in a state of nature?

Locke has defined the state of nature as a state where every men has his own freedom to make his decisions and to dispose their persons and possession which fits in the bounds of law of nature.

In this state no one has to take permission from anyone to act or to make any decision related to anyone. Since no one has control over anyone's act, hence all men are equal in this state of nature.