The word taciturn ends with the sound "-urn." Therefore, the option that rhymes with the word taciturn should also have a similar ending sound. Let's analyze the options:
rerun - Ends with "-un." The ending sound is not similar to "-urn." Therefore, it does not rhyme.
tarn - Ends with "-arn." This ending sound is different from "-urn." Hence, it does not rhyme.
around - Ends with "-ound." This ending sound does not match "-urn." Therefore, it does not rhyme.
burn - Ends with the exact sound "-urn," which is the same as the ending of taciturn. Hence, it rhymes with taciturn.
Therefore, the word burn rhymes with the word taciturn.