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Don't fear the dog that's barking.
Literal
Barking-is dog [object-を] don't-fear.
吠えている犬 ('the dog that is barking') uses the ~ている relative clause. 恐れる ('to fear, to be afraid of') takes を for the feared object (unlike 怖がる, the expressive counterpart). 恐れるな is the negative imperative 'don't fear.' A gentler rephrasing of the 'barking dogs' proverb.