15 is related to 20 following a certain logic. Following the same logic, 6 is related to 8. Which of the following numbers is related to 12 using the same logic?

The correct answer is Option 9.

Let us analyze the relationship between the first pair of numbers: 15 and 20.
We can observe the ratio of the two numbers:
$\frac{15}{20}=\frac{3}{4}$

Now let us check the relationship between the second pair of numbers: 6 and 8.
The ratio is:
$\frac{6}{8}=\frac{3}{4}$

Both pairs of numbers share the same simplified ratio of 3 : 4. That is:
$\text{First Number}:\text{Second Number}=3:4$

Following the same logic, we want to find the number, let's call it $x$, that is related to 12.
This gives us the proportion:
$\frac{x}{12}=\frac{3}{4}$

To solve for $x$, we multiply both sides of the equation by 12:
$x=12\times \frac{3}{4}$
$x=3\times 3$
$x=9$

Therefore, the number related to 12 using the same logic is 9.