Explanation

Since the blank refers to something delivered by a poet or orator and meant to lavish praise, you need something like poem of praise or speech of praise. Three of the choices are the wrong kind of writing: Both an elegy and a jeremiad express lamentation, and a philippic expresses condemnation, so eliminate choices (B), (D), and (E). A compendium is a brief summary, so eliminate choice (A). Both encomium and panegyric can mean poem or speech
of praise, so choices (C) and (F) give you appropriate, equivalent sentences.

Hence options C and F are correct!