Primaries, the secret ballot, and the use of
referendum and recall were efforts made during
the progressive era to
(1) preserve the power of political machines
(2) provide equal political rights for native
american indians
(3) protect states rights against federal power
(4) increase citizen participation in government

(4) Increase citizen participation in government

Primary: a way for citizens to vote for new government officials, not too influenced by party leaders
Secret Ballot: keeping a voter's votes private from others
Recall: a way for citizens to remove a government official from office
Referendum: a way for citizens to vote for or against something proposed by the legislature

During the Progressive Era, many local governments were lead by corrupt political machines. They would rig elections in their favor as well as threaten those who voted against them. Many would appoint their supporters who weren't usually qualified to government positions as incentive to vote for them (I don't know if you care but that's called the spoils system).

It's not (1) because the whole point of primaries, secret ballots, recalls, and referendums was so political machines were not dominating
It's not (2) because none of this has a lot to do with Native Americans
It's not (3) because the political machines were a local government problem, not federal
It IS (4) because by getting more people involved in the government, they can elect qualified officials, vote on laws that best benefit the people, and minimize corruption.