GOAL: find the value of $\frac{x}{y}$

Given: $\frac{1}{4x} + \frac{1}{y}$= $\frac{1}{3}$ $*$ $(\frac{1}{x} + \frac{1}{y})$

First expand right side to get: $\frac{1}{4x}+\frac{1}{y} = \frac{1}{3x} + \frac{1}{3y}$

Next, eliminate the fractions.
To do so, we'll examine the denominators - the least common multiple of $4x$, $y$, $3x$ and $3y$ is $12xy$.

So, we'll multiply both sides of the equation by $12xy$ to get: $3y + 12x = 4y + 4x$

Rearrange and simplify to get: $8x = y$

Divide both sides by $y$ to get: $\frac{8x}{y} = 1$

Divide both sides by $8$ to get: $\frac{x}{y} = \frac{1}{8}$

So, $x : y = 1 : 8$

Answer: D

Cheers,
Brent