Solve the Fraction Equation: Finding the Denominator in 16ab/? = 2b

Complete the corresponding expression for the denominator

$\frac{16ab}{?}=2b$

After examining the problem, proceed to write the expression on the right side as a fraction (using the fact that dividing a number by 1 does not change its value):

$\frac{16ab}{?}=2b \\ \downarrow\\ \frac{16ab}{?}=\frac{2b}{1}$

Remember the fraction reduction operation,

In order for the fraction on the left side to be deemed reducible, we want all the terms in its denominator to have a common factor. Additionally, we want to reduce the number 16 in order to obtain the number 2. Furthermore we want to reduce the term $a$ from the fraction's denominator given that in the expression on the right side it does not appear. Therefore we will choose the expression:

$8a$

Due to the fact that:

$16=8\cdot 2$

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

$\frac{16ab}{?}=\frac{2b}{1} \\ \downarrow\\ \frac{\not{16}\not{a}b}{\textcolor{red}{\not{8}\not{a}}}\stackrel{?}{= }\frac{2b}{1} \\ \downarrow\\ \boxed{\frac{2b}{1}\stackrel{!}{= }\frac{2b}{1} }$

Therefore this choice is indeed correct.

In other words - the correct answer is answer B.