Left-side mouth radical - pictograph of an open mouth. The indexing radical here, marking 吠 as a sound-from-the-mouth verb, alongside 叫 call, 喊 shout, 唱 sing, 哭 cry. Barking is mouth-noise par excellence, so the radical does direct semantic duty.
Right-side 犬 - pictograph of a dog with its tail curled up. Together with the mouth on the left this is a textbook compound ideograph: dog + mouth = barking. No phonetic element involved; 吠 reads fèi by historical attachment to this picture, not by sound-borrowing. The cleanest two-component meaning combo in the canine family.
