The correct answer is:   [A]:  
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            " assonance " .
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<u>Note</u>:  Lines 3 and 4 ;  as follows:
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     " And many an eye has dance to see
       That banner in the sky ; " 
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Note that "assonance" refers to the "repetition of vowel sounds" ; that occur "with" words that are close by.
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Note the following words that in "lines 3 and 4" that contain that; 
in bold font; as follows:
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     " <u>A</u>nd m<u>a</u>ny <u>a</u>n eye h<u>a</u>s d<u>a</u>nce to see
       Th<u>a</u>t b<u>a</u>nner in the sky ; " 
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The presents of "repetition of [a] vowel sound" is quite evident within "lines 3 and 4" — as shown above.
{<u>Note</u>:  Try reading the lines aloud and notice 'vowel sounds' that are indicated bold font and underlined — as shown above.}.
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"Alliteration" would be incorrect; since "alliteration" would refer to the present of the repetition of the same consonant sounds; or the same vowel sounds; at the beginning of the first syllables of, words that follow each other—as well as words that appear close together.  There is no evidence of this in "lines 3 and 4" of the given passage.  
We can rule out "end rhyme" ; since "see" and "sky" do not "rhyme" —nor do "dance to sea" and "in the sky"— which occur at the end of lines 3 and 4.
  We can rule out "onomatopoeia" — since there is no evidence of the use of words that sound like themselves (i.e. no evidence of words such as "rattle, jolt, murmur, gargle, buzz, chirp — within "lines 3 and 4."}.  
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Hope this is helpful to you!
      Wishing you the best!
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