Solve the Fraction Equation: Finding the Denominator in (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,

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 get 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 get 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 indeed correct.

In other words - the correct answer is answer D.