To solve this problem, let's analyze the question:

Problem Breakdown:

1. Average Score: The average score of 12 students is 80. Therefore, the total score of all 12 students is: $\text{Total Score} = 12 \times 80 = 960$

2. Groups:

   • 6 students have an average of 75. The total score for these 6 students is: $6 \times 75 = 450$
   • 4 students have an average of 90. The total score for these 4 students is: $4 \times 90 = 360$

3. Remaining Students:

   • There are $12 - 6 - 4 = 2$ students left.
   • The total score of these 2 students is: $960 - 450 - 360 = 150$

4. Range of Scores:

   • The question asks for the minimum possible score (P) of one of the remaining 2 students.
   • The smallest score possible starts from 0, with the constraint that the total score of the 2 students is 150.

Calculation for Minimum Score (P):

• To minimize $P$, assign the largest possible score to the other student (out of the two). The maximum possible score is capped at 100 (as stated in the question). If one student gets 100, the score of the other student will be: $150 - 100 = 50$ Thus, the minimum possible score (P) is $50$.

Comparing $P$ and $Q$:

• $P = 50$ (calculated above).
• $Q = 50$ (given in the table).

Conclusion:

The correct relationship is: $\boxed{(C) \, P = Q}$

Do you want further clarification or detailed steps?
Here are 5 related questions to expand your understanding:

1. What happens if the score range is extended beyond 0–100?
2. How do we calculate the maximum score of one student in this scenario?
3. What is the role of constraints in minimizing or maximizing scores?
4. How does the average formula affect score distributions?
5. Can this method be applied to more complex distributions?

Tip: Always check if minimizing or maximizing a value satisfies the constraints provided in the problem!