In Act 3 Scene 4 of Hamlet, by analogy, what does Hamlet mean by saying "If thou canst mutine ... and melt in her own fire"?HAMLET: Eyes without...

When you are looking at a quote like this, you need to be
careful to consider what the pronouns are referencing.  In this case you need to know what "thou"
stands for shame from the previous full line.  He is asking his mother where her shame is for she
should be ashamed of her behavior in marrying Claudius.  Hamlet is questioning whether there is
shame living in her bones (a synecdoche to her body and soul).  Hamlet is commenting on how there
are impulses in our human nature that are in conflict with our virtue--virtue melts like wax in
the fire of the evil in our nature.  Hamlet is suggesting that this is especially true in youth
when there is more impulsive and irrational behavior.  He wants his mother to act her age, find
her virtuous nature, and reject Claudius and her sinful actions with him.