(i) To find \(P(Q)\), we need the pairs \((a, b)\) such that \(a \times b = 24\). The possible pairs are \((2, 12), (3, 8), (4, 6), (6, 4), (8, 3), (12, 2)\). There are 6 favorable outcomes. The total number of outcomes when two dice are thrown is \(12 \times 12 = 144\). Thus, \(P(Q) = \frac{6}{144} = \frac{1}{24}\).

(ii) For \(P(R)\), both numbers must be greater than 8. The numbers greater than 8 are 9, 10, 11, and 12. Thus, there are 4 choices for each die, giving \(4 \times 4 = 16\) favorable outcomes. Therefore, \(P(R) = \frac{16}{144} = \frac{1}{9}\).

(iii) Events \(Q\) and \(R\) are exclusive if they cannot occur simultaneously. Since \(R\) requires both numbers to be greater than 8, and none of the pairs for \(Q\) satisfy this, \(P(R \cap Q) = 0\). Thus, \(R\) and \(Q\) are exclusive.

(iv) Events \(Q\) and \(R\) are independent if \(P(R \cap Q) = P(R) \times P(Q)\). Since \(P(R \cap Q) = 0\) and \(P(R) \times P(Q) \neq 0\), they are not independent.