When equality and liberty meet conflict, which one goes first?I want to support equality.

I love the way this question is phrased.  It's quite
classic and really epic in its phraseology.  I do think that some level of specifics are
needed in terms of time period, historical context, some level of conditions are all
needed in order to really effectively answer this
question.

Specificity is needed because there might need to
be a clear distinction that indicates there is a potential tradeoff between the two. 
Usually, both concepts have been presented to complement one another.  For example, the
American Revolution stressed both in The Declaration of Independence.  Both equality and
liberty were seen as needed ends that were being denied by the British government and
both served as animating forces in need for the colonists to be free.  In the French
Revolution, both were mentioned as complementing symbols that were being denied by the
Monarchy.  There has been a tendency to see equality as something whereby freedom is
applied to all.  In this context, both are seen from a historical point of view as
complementary to one another, a necessary partnership that has ushered change into a
political and social setting.

If there is a simple answer
to the question, it would have to be that it depends.  Part of the reason it depends
lies in the strength of the political authority and what fundamental beliefs the
political structure wishes to enforce.  Governments sometimes have used one as a
potential "cover" to enforce their own agendas at the cost of the theoretical
principle.  For example, Nazi Germany asserted the fundamental liberty of the German
state, the fatherland.  In this assertion of a collectivized notion of freedom
predicated upon inequality, "freedom" came at the cost of others' inequality.  In
American History, the end of the Civil War and the passage of the Civil War Amendments
provided a national base of "equality" from the most theoretical point of view.  Yet,
there was still a sense of inequality and denial of individual liberty for people of
color that was not rectified for nearly a century after the end of the Civil War
conflict.  In both settings, the political institution paraded one concept in an
inauthentic manner to the detriment of the perceived expectation of the other idea.  It
is for this reason why more detail and more specificity is needed in a greatly worded
question.