This problem can be solved by translating the verbal statement into an algebraic equation and then isolating the ratio $\frac{x}{y}$.
1. Translate the equation

The problem states: $\(2 x+3 y=175\) %$ of $8 x$. Since $175 %=1.75$ (or $\(\frac{175}{100}\)$ ), we can write:

$$
\(2 x+3 y=1.75 \times 8 x\)
$$

2. Simplify the right side

First, calculate $\(1.75 \times 8\)$ :

$$
\(1.75 \times 8=\frac{7}{4} \times 8=7 \times 2=14\)
$$


Now the equation is:

$$
\(2 x+3 y=14 x\)
$$

3. Isolate $x$ and $y$

Subtract $2 x$ from both sides to group the $x$ terms together:

$$
\(\begin{gathered}
3 y=14 x-2 x \\
3 y=12 x
\end{gathered}\)
$$

4. Find the ratio $\(\frac{x}{y}\)$

To find $\(\frac{x}{y}\)$, divide both sides by 12 and by $y$ (given $\(x y \neq 0\)$, we know $\(y \neq 0\)$ ):

$$
\(\frac{3}{12}=\frac{x}{y}\)
$$


Simplify the fraction $\(\frac{3}{12}\)$ :

$$
\(\frac{1}{4}=\frac{x}{y}\)
$$


Final Answer: The ratio $\(\frac{x}{y}\)$ is $\(1 / 4\)$, which corresponds to option $\(\mathbf{D}\)$.