b. The coffee taster will prove each batch to be sure that it is robust and full-flavored. This option is the correct one.
The word prove in the second line of the stanza is used to mean taste . Coffee can be tasted, and the poet wants his beloved to taste /prove the pleasures of nature: " ......valleys, groves , hills....yields."
The correct answer is (B). In this particular context, "prove" means "experience", "be in contact with"