Solve the Fraction Equation: Finding the Denominator in 10a/? = 6a/3

Let's examine the problem, first let's note that the fraction on the right side can be reduced:

$\frac{10a}{?}=\frac{\not{6}a}{\not{3}} \\ \downarrow\\ \frac{10a}{?}=\frac{2a}{1}$

where we used the fact that:

$6=2\cdot3$

Now let's think logically, and remember the process of reducing a fraction,

Note that both in the numerator of the expression on the right side and in the numerator of the expression on the left side exists the expression $a$, therefore in the expression we are looking for there are no variables (since we don't want to reduce them from the expression in the numerator on the left side),

Next, we ask which number was chosen to put in the denominator of the expression on the left side so that when reduced with the number 10 will yield the number 2, the answer to this is of course - the number 5,

Because:

$10=2\cdot 5$

Let's verify that this choice indeed gives us the expression on the right side:

$\frac{10a}{?}=\frac{2a}{1} \\ \downarrow\\ \frac{\not{10}a}{\textcolor{red}{\not{5}}}\stackrel{?}{= }\frac{2a}{1} \\ \downarrow\\ \boxed{\frac{2a}{1}\stackrel{!}{= }\frac{2a}{1}}$

therefore this choice is indeed correct.

In other words - the correct answer is answer C.