Given Numbers:
453 : 99

Pattern:
To find the related number for the second set of numbers, we need to identify the pattern or relationship between the first set of numbers.

Analysis:
Let's analyze the given numbers and try to identify any pattern or relationship between them.

First Set of Numbers:
453

Prime Factors of 453:
453 = 3 × 151

Second Set of Numbers:
99

Prime Factors of 99:
99 = 3 × 3 × 11

Pattern Identification:
By analyzing the prime factors of the given numbers, we can see that:
- The first set of numbers (453) has two prime factors: 3 and 151.
- The second set of numbers (99) has three prime factors: 3, 3, and 11.

Pattern Extension:
Based on the pattern identified, we can extend it to the second set of numbers (642) to find the related number.

Prime Factors of 642:
642 = 2 × 3 × 107

Pattern Application:
Now, applying the pattern we observed, we can see that:
- The first set of numbers has two prime factors (3 and 151).
- The second set of numbers has three prime factors (3, 3, and 11).
- The third set of numbers (related number) should have four prime factors.

Related Number:
To find the related number, we need to find a number that has four prime factors.

Option Analysis:
Let's analyze the options provided:

a) 764
Prime Factors: 2 × 2 × 191 (3 prime factors)

b) 346
Prime Factors: 2 × 173 (2 prime factors)

c) 867
Prime Factors: 3 × 17 × 17 (3 prime factors)

d) 396
Prime Factors: 2 × 2 × 3 × 3 × 11 (5 prime factors)

Conclusion:
From the given options, option d) 396 is the only number that has four prime factors, which matches the pattern we observed.

Therefore, the correct answer is option d) 396.