Solve the Fraction Equation: Finding the Denominator in (16x-4)/? = 4

Complete the corresponding expression for the denominator

$\frac{16x-4}{?}=4$

Let's examine the problem, first we'll write the expression on the right side as a fraction (using the fact that dividing a number by 1 does not change its value):

$\frac{16x-4}{?}=4 \\ \downarrow\\ \frac{16x-4}{?}=\frac{4}{1}$

Now let's think logically, and remember the fraction reduction operation,

In order for the fraction on the left side to be reducible, we want all the terms in its numerator to have a common factor, so first we'll check if it can be factored, and we'll identify that it indeed can be factored, using finding a common factor:

$$$\frac{16x-4}{?}=\frac{4}{1} \\ \frac{4(4x-1)}{?}=\frac{4}{1}$

Now let's examine again the expression on the left side,

Note that to obtain the number 4 in the fraction's numerator after reduction, we need to reduce only the algebraic expression (two-term):

$4x-1$

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

$\frac{4(4x-1)}{?}=\frac{4}{1} \\ \downarrow\\ \frac{4(4x-1)}{\textcolor{red}{4x-1}}\stackrel{?}{= }\frac{4}{1} \\ \downarrow\\ \boxed{\frac{4}{1} \stackrel{!}{= }\frac{4}{1} }$

Therefore this choice is correct.

In other words - the correct answer is answer D.