The word "心急火燎" is formed by directly combining two two-character phrases: "心急" meaning "anxious" (with "心" for heart and "急" for urgent) and "火燎" meaning "fire burning" (with "火" for fire and "燎" for to burn). This combination creates a literal juxtaposition where mental urgency is metaphorically intensified by the image of fire, resulting in an idiom that conveys extreme impatience or agitation.