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I hurry [someone] along with dinner.
Literal
Dinner [object-を] hurry-up-[cause-させる].
A curious short sentence. せかせる is a variant of 急かす/急かせる ('to rush, hurry someone up') — specifically used to press someone to hurry with an action. Here 夕飯 is the matter one is hurrying the other person about. Without context, the subject is unclear — a parent might be 'rushing the kids through dinner,' or the speaker might be rushing a spouse to cook faster. Useful for the verb itself.