If 2 : 4 :: 4.6 : x and 4 : 16 :: 2 : y, what is the ratio of x to y?

The correct answer is 23 : 20.

Let us solve the problem step-by-step.

First, we are given the proportion:
$2:4::4.6:x$
This can be written as an equation of fractions:
$\frac{2}{4}$
Simplifying $\frac{2}{4}$ gives:
$\frac{1}{2}$
Cross-multiplying to solve for $x$:
$x=2\times 4.6=9.2$

Second, we are given the proportion:
$4:16::2:y$
This can be written as:
$\frac{4}{16}$
Simplifying $\frac{4}{16}$ gives:
$\frac{1}{4}$
Cross-multiplying to solve for $y$:
$y=4\times 2=8$

Now, we need to find the ratio of $x$ to $y$:
$x:y=9.2:8$
To express this ratio in simplest integer form, we multiply both terms by 10 to eliminate the decimal:
$92:80$
Now, we find the greatest common divisor (GCD) of 92 and 80 to simplify the ratio. Dividing both terms by 4:
$\frac{92}{4}$ : $\frac{80}{4}$
This simplifies to:
$23:20$

Thus, the ratio of $x$ to $y$ is 23 : 20.