The correct answer is D) The tanks are partially filled with liquid cargo. When a vessel has cross-connected deep tanks that are partially filled with liquid cargo, the cross-connection valve should be closed. This is because the motion of the vessel can cause the liquid to shift between the tanks, creating an unstable condition that could lead to free surface effect and potential capsize. Closing the cross-connection valve isolates the tanks and prevents this liquid shifting, ensuring the vessel's stability is maintained. The other answer choices are incorrect because: A) Tanks above the waterline do not pose the same stability risk; B) Fully filled tanks, whether above or below the waterline, also do not have the same liquid shifting concerns; and C) Dry cargo does not exhibit the same free surface effect as liquid cargo.