Step 1: Recall the physical basis of the two logs:
The neutron tool counts hydrogen atoms in the pore fluid and converts that count into an apparent porosity, $\phi_N$. The density tool measures bulk density and converts it into porosity, $\phi_D$, using an assumed fluid and matrix density. Any fluid whose hydrogen index or density differs from the assumption used in calibration will make $\phi_N$ and $\phi_D$ disagree, and the pattern of disagreement is diagnostic of the fluid type.
Step 2: Test option A, gas zone, using the hydrogen index argument:
Gas at reservoir conditions has a hydrogen index that can be a small fraction of that of liquids, so it makes the neutron tool report far too little porosity while density porosity stays close to the true value. The result is $\phi_N \ll \phi_D$, the classic crossover, and this is the standard way gas zones are picked out, so option A holds.
Step 3: Test option B, shale distribution:
Although shale does distort both the neutron and density response through bound water and mineral effects, the practical tool for mapping how much shale is present and how it is distributed bed by bed is the gamma ray or SP curve, not the neutron density pair by itself. Since the question asks what is inferred using the cross plot specifically, shale distribution is not the direct output, so option B does not hold.
Step 4: Test option C, water zone:
Water has a hydrogen index near 1, essentially matching the neutron tool calibration fluid, so $\phi_N \approx \phi_D$ in a clean water bearing interval and the points fall along the expected lithology line with no crossover. Analysts use this absence of separation as the marker for a water zone, so option C holds.
Step 5: Test option D, oil zone:
Because oil also carries a hydrogen index near 1, an oil zone produces nearly the identical $\phi_N \approx \phi_D$ pattern seen in a water zone. The cross plot has no way to separate the two liquids from each other, so it cannot be used to specifically infer an oil zone, and option D fails.
Final Answer:
\[ \boxed{\text{Options A and C, gas zone and water zone}} \]