The correct answer is D) gooseneck vents and flame screens. Cargo tanks carrying grades D or E liquids on tank barges are required to be ventilated with gooseneck vents and flame screens. This is in accordance with the requirements set forth in 46 CFR 32.55, which specifies the ventilation system for cargo tanks carrying flammable or combustible liquids. Gooseneck vents with flame screens are designed to prevent the entry of sparks or flames into the cargo tank, which is crucial for the safe handling of these hazardous liquids. The other options are incorrect because forced draft blowers (A) are not the required ventilation method, branch vent lines and a vent header (B) are not specific to grades D or E liquids, and pressure-vacuum relief valves (C) are a separate safety feature and not the primary ventilation method.