The given problem requires us to find the average marks of all combinations of three sections. To solve this problem, we need to follow the steps outlined below:

Step 1: Determine the number of students in each section.
We are given the ratio of the number of students in sections P, Q, R, and S as 2:3:6:4. Let's assume the common ratio as x. Therefore, the number of students in each section will be:
P = 2x
Q = 3x
R = 6x
S = 4x

Step 2: Determine the total number of students.
To find the total number of students, we add up the number of students in each section:
Total number of students = P + Q + R + S
Total number of students = 2x + 3x + 6x + 4x
Total number of students = 15x

Step 3: Determine the average marks of each section.
We are given the ratio of the average marks of sections P, Q, R, and S as 5:4:3:2. Let's assume the common ratio as y. Therefore, the average marks of each section will be:
Average marks of P = 5y
Average marks of Q = 4y
Average marks of R = 3y
Average marks of S = 2y

Step 4: Determine the total marks for each section.
To find the total marks for each section, we multiply the average marks by the number of students in that section:
Total marks for P = Average marks of P * Number of students in P
Total marks for Q = Average marks of Q * Number of students in Q
Total marks for R = Average marks of R * Number of students in R
Total marks for S = Average marks of S * Number of students in S

Step 5: Determine the average marks of all combinations of three sections.
To find the average marks of all combinations of three sections, we need to consider the combinations of three sections from P, Q, R, and S. There are a total of 4C3 = 4 combinations possible. Let's consider each combination:

Combination 1: PQR
Average marks of combination 1 = (Total marks for P + Total marks for Q + Total marks for R) / (Number of students in P + Number of students in Q + Number of students in R)

Combination 2: PQS
Average marks of combination 2 = (Total marks for P + Total marks for Q + Total marks for S) / (Number of students in P + Number of students in Q + Number of students in S)

Combination 3: PRS
Average marks of combination 3 = (Total marks for P + Total marks for R + Total marks for S) / (Number of students in P + Number of students in R + Number of students in S)

Combination 4: QRS
Average marks of combination 4 = (Total marks for Q + Total marks for R + Total marks for S) / (Number of students in Q + Number of students in R + Number of students in S)

Let's calculate the average marks for each combination using the given information and formulas mentioned above.