Solve the Fraction Equation: Finding the Denominator in 18b/? = 3b/2a

$$Examine the given problem:

$\frac{18b}{?}=\frac{3b}{2a}$

Remember the fraction reduction operation:

Let's start with the numbers:

In order for the fraction on the left side to be reducible, all the terms in its denominator must have a common factor,

Additionally, we want to reduce the number 18 to obtain the number 3 in the fraction's numerator. Furthermore we also want the number 2 in the fraction's denominator following its reduction.

For this, we'll represent the number 18 - which is in the numerator of the left side as a product of numbers where one of them is the number 3. Remember that the number which we multiply by 3 in order to obtain the number 18 is the number 6:

$$$\frac{18b}{?}=\frac{3b}{2a}\\ \downarrow\\ \frac{\textcolor{blue}{3}\cdot\textcolor{orange}{6}\cdot b}{?}=\frac{\textcolor{blue}{3}b}{2a}$

Now following the reduction only the number 3 remains in the numerator of the fraction on the left side. However in the fraction's denominator the number 2 remains, meaning - that the number 6 can be reduced. Therefore the obvious choice is the number 12, due to the fact that:

$12=2\cdot\textcolor{orange}{6}$

Let's continue to the letters:

Examine the expression once again:

$\frac{18b}{?}=\frac{3b}{2a}$

$$We want to obtain the term $a$, in the denominator of the fraction on the right side. Note that this term is not found in the expression in the numerator of the fraction on the left side, therefore for the letters we'll choose the following expression:

$a$

In summary, for both the letters and numbers together we'll choose the expression:

$\boxed{12a}$

Let's verify that from this choice we obtain the expression on the right side:

$\frac{18b}{?}=\frac{3b}{2a} \\ \downarrow\\ \frac{18b}{\textcolor{red}{12a}}\stackrel{?}{= }\frac{3b}{2a} \\ \frac{3\cdot\textcolor{orange}{\not{6}}\cdot b}{2\cdot\textcolor{orange}{\not{6}}\cdot a}=\frac{3b}{2a} \\ \downarrow\\ \boxed{\frac{3b}{2a}\stackrel{!}{= }\frac{3b}{2a} }$

Therefore this choice is indeed correct.

Meaning - the correct answer is answer C.