Identify the product required

We need the reagent/condition $X$ such that: $P_4 \xrightarrow{X} P_4O_6$

$P_4O_6$ is phosphorus(III) oxide (formed when phosphorus burns in a limited supply of oxygen).

Recall the relevant reactions of phosphorus with oxygen

• In excess oxygen: $P_4 + 5O_2 \rightarrow P_4O_{10}$
• In limited oxygen: $P_4 + 3O_2 \rightarrow P_4O_6$

So, to obtain $P_4O_6$ selectively, oxygen must be available in a restricted amount, not in excess.

Evaluate each option

Option A: Dry $O_2$

Pure dry oxygen provides abundant oxygen. Phosphorus burns vigorously and tends to form the higher oxide: $P_4O_{10}$ So this is not selective for $P_4O_6$.

Option B: A mixture of $O_2$ and $N_2$

Mixing $O_2$ with inert $N_2$ effectively dilutes oxygen, creating a limited oxygen atmosphere. Under such controlled oxygen supply, phosphorus forms: $P_4O_6$ Hence this option is correct.

Option C: Moist $O_2$

Moisture is not suitable because phosphorus oxides can undergo hydrolysis, and oxygen is still available. This will not selectively give pure $P_4O_6$.

Option D: $O_2$ in the presence of aqueous NaOH

In aqueous/basic medium, phosphorus and its oxides can undergo side reactions/disproportionation or hydrolysis. This is not a condition for selective formation of $P_4O_6$.

Conclusion

The correct condition is a diluted oxygen atmosphere, i.e. a mixture of $O_2$ and $N_2$.

Therefore, the correct answer is: $\boxed{\text{B}}$