public boolean isSummer(String month)

Given the name of a month, determine whether it is a summer month
("June", "July" or "August"). If it is, return true. Otherwise return false.

Although startsWith() can be used to solve many problems,
occasionally it is not the best choice.

Sometimes the best choice is equals(), as for this problem.

public boolean isSummer(String month) {
  boolean summer = false;
  if (month.equals("June")) {
    summer = true;
  }
  if (month.equals("July")) {
    summer = true;
  }
  if (month.equals("August")) {
    summer = true;
  }
  return summer;
}

NOTE: that if you have 3 successive IF statements, they can be
collapsed into a single statement if you separate them with || (OR).

public boolean isSummer(String month) {
  boolean summer = false;
  if ( month.equals("June") || month.equals("July") || month.equals("August") ) {
    summer = true;
  }
  return summer;
}