The numbers 6 and 18 are related by a particular arithmetic operation. Using the same relationship, 4 is related to which of the following numbers?

Introduction / Context:
This number analogy checks understanding of simple arithmetic patterns. You are given that 6 is related to 18 and must find how 4 is related to another number in exactly the same way. Identifying the operation that maps 6 to 18 is the key step.

Given Data / Assumptions:
1) The first pair is 6 and 18.
2) The second pair involves 4 and an unknown number from 14, 6, 16, or 8.
3) The operation is likely to be a simple multiplication or a square based pattern because 18 is a multiple of 6.

Concept / Approach:
One common approach is to check multiples of 6 and also powers. 6 times 3 equals 18, but if we apply the same linear rule to 4, we get 12, which is not in the options. Another idea is to check 6 squared, which is 36, then to see if 18 is related as half of that. If so, we might have the rule n squared divided by 2. Applying this to 4 would give a candidate answer. We choose the simplest rule that fits both pairs and one of the options.

Step-by-Step Solution:
Step 1: Compute 6 squared, which is 6 * 6 = 36. Step 2: Check whether 18 relates to 36. Notice that 18 is exactly half of 36, that is 36 divided by 2. Step 3: Conclude that the rule can be written as n squared divided by 2. Step 4: Now apply this rule to 4. Compute 4 squared, which is 4 * 4 = 16. Step 5: Take half of 16, which is 16 divided by 2 equal to 8. Step 6: Confirm that 8 is among the answer choices and that no other option fits the n squared divided by 2 rule.

Verification / Alternative check:
Try alternative simple rules for completeness. If the rule were multiplication by 3, then the second number should be 12, not present among the options. If the rule were adding 12, 6 plus 12 equals 18 but 4 plus 12 equals 16, which is an option, yet does not use squaring and does not look as structured. The n squared divided by 2 rule feels more symmetric and typical for such a question.

Why Other Options Are Wrong:
Option 14 does not arise from squaring 4 or any simple multiple that matches the first pair. Option 6 would be 4 plus 2, which does not relate to 6 and 18. Option 16 is 4 squared, but then the first pair would require that 6 be mapped directly to 36, which is not given. Only 8 arises naturally from the n squared divided by 2 rule applied consistently.

Common Pitfalls:
A common mistake is to jump to multiplication by 3 and then try to force a rule that does not fit the options. Another error is to focus solely on addition, ignoring the possibility of squaring. Always check both multiplication based and exponent based rules in number analogies, especially when one number seems to be roughly the square or half square of the other.

Final Answer:
Thus, using the same relationship, 4 is related to 8. The correct answer is 8.