Please give an explanation of lines 12-19 of the poem "My Last Duchess" by Robert Browning.

In Robert Browning's poem "My Last Duchess," Browning
describes a duke who is speaking to the representative of a future wife for himself. 
This duke, as a sort of warning to the representative of his bride, shows the painting
of his previous spouse, now deceased, and describes what he believes to have been her
weak and flirtatious character.  In doing so, he is able to convey the message of
warning that his new wife had better be better behaved, or
else.

In lines 12-19, he mentions that the representative
might have noticed the coy and excited expression on the former wife's face in the
painting.  The duke says that many have wondered and asked that question, and that it
wasn't her husband alone that made her appear to be so happy.  Rather, she seemed to
give delighted glances to a lot of people, for a lot of reasons.  For example, the
painter of the painting (Fra Pandolf) might have told her that part of the mantle in the
painting was covering too much of her wrist, or that he was incapable of painting the
flush of color along her throat.  These little things that people said to her often made
her blush with joy.  The rest of the poem goes on to indicate that the duke highly
disapproved of his wife's joyous behavior; he considered it inapproprate that she should
be happy around anyone other than him.  So, he "gave commands," and the wife, the reader
has to assume, was killed.  This was to warn his future bride that she had beeter not
behave that way.

A bit bizarre, yes, but it certainly makes
for an entertaining story for a poem.  I hope that helped a bit; good
luck!