give an explanation of these lines'Half-flush that dies along her throat:' such stuffWas courtesy, she thought, and cause enoughFor calling up that...

The speaker in the poem "My Last Duchess" is presumably
the Duke, her husband. Throughout the poem, he expresses his displeasure at the young
lady's joy.  She finds joy in things like a sunset ("the dropping of the daylight...)
and cherries from an orchard.  For the Duchess, these were simple things of beauty, and
worthy of her joy.  It might also be assumed that she is blissfully unaware of the
Duke's unhappiness.

The Duke, in turn, appears to harbor
some jealously, not only at the "officious fools" who bring her cherries, but also
towards innocent symbols of joy such as the sunset.  For the Duke, the money and
pleasure that he provides her should be the only things that make the Duchess
happy.

The fact that these do not take priority in her
pleasure drives the Duke to distraction, and he meticulously lists everything that makes
her heart glad "too soon" and that calls that "spot of joy" to her cheek.  In short, he
is jealous and past the verge of letting this jealously get the better of
him.