To find the remainder when (7(4n + 3))(6n) is divided by 10, we need to simplify the expression and then divide it by 10 to find the remainder.

Simplifying the expression:
(7(4n + 3))(6n)
= 7 * (4n + 3) * 6n
= 42n * (4n + 3)
= 168n^2 + 126n

Dividing by 10:
To find the remainder when dividing by 10, we only need to consider the units digit of the expression, as the remainder will be the same whether we divide by 10, 100, 1000, etc.

The units digit of 168n^2 will always be 8, as the units digit of any number squared will always be the same as the units digit of the original number.

The units digit of 126n will depend on the value of n. Let's consider the possible values of n and their corresponding units digits:

- For n = 1, the units digit is 6.
- For n = 2, the units digit is 2.
- For n = 3, the units digit is 8.
- For n = 4, the units digit is 4.
- For n = 5, the units digit is 0.
- For n = 6, the units digit is 6.
- For n = 7, the units digit is 2.
- For n = 8, the units digit is 8.
- For n = 9, the units digit is 4.

From this pattern, we can see that the units digit of 126n repeats every 4 values of n. Therefore, for any positive integer n, the units digit of 126n will be the same as the units digit of 126n when divided by 4.

Calculating the remainder when dividing 126 by 4:
126 ÷ 4 = 31 remainder 2

Therefore, the units digit of 126n will be the same as the units digit of 126(4n) when divided by 4, which is 2.

Now we can find the units digit of the entire expression:
168n^2 + 126n
= 8 + 2 (since the units digit of 168n^2 is always 8 and the units digit of 126n is always 2)
= 10

The units digit of the expression is 10, which means the remainder when dividing by 10 is 0.

Therefore, the correct answer is option D) 8.