Verified answer

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a) (2, 4) ∈ R:

To check if (2, 4) is in R, we need to verify if a = b - 2 holds true and if b > 6 holds true.

For (2, 4), a = 2 and b = 4. The first condition a = b - 2 is not satisfied because 2 is not equal to 4 - 2. Additionally, b > 6 is not satisfied because 4 is not greater than 6. Therefore, (2, 4) is not in R.

b) (3, 8) ∈ R:

For (3, 8), a = 3 and b = 8. The first condition a = b - 2 is satisfied because 3 is not equal to 8 - 2. Furthermore, b > 6 is satisfied because 8 is greater than 6. Therefore, (3, 8) is not  in R.

c) (6, 8) ∈ R:

For (6, 8), a = 6 and b = 8. The first condition a = b - 2 is satisfied because 6 is equal to 8 - 2. Also, b > 6 is satisfied because 8 is greater than 6. Therefore, (6, 8) is in R.

d) (8, 7) ∈ R:

For (8, 7), a = 8 and b = 7. The first condition a = b - 2 is not satisfied because 8 is not equal to 7 - 2. Additionally, b > 6 is not satisfied because 7 is not greater than 6. Therefore, (8, 7) is not in R.

So, the correct answer is option (c) (6, 8) ∈ R.