The problem shows two similar rectangular prisms. To find the value of $y$, we use the fact that for similar figures, the corresponding side lengths are proportional. Let's define the sides of the prisms based on the labels given.

For the larger prism:

• One side = 8 inches,
• Another side = 12 inches,
• Another side = 3 inches.

For the smaller prism:

• One side = $y$ inches (corresponds to 8 inches of the larger prism),
• One side = $q$ inches (corresponds to 12 inches of the larger prism),
• One side = $x$ inches (corresponds to 3 inches of the larger prism).

The ratio of corresponding sides must be equal. Let's set up a proportion using the dimensions where we know the values from both prisms.

$\frac{8 \, \text{in}}{y \, \text{in}} = \frac{12 \, \text{in}}{q \, \text{in}} = \frac{3 \, \text{in}}{x \, \text{in}}$

To solve for $y$, we need the ratio $\frac{8}{y} = \frac{3}{x}$. Once we know $x$, we can directly solve for $y$.

Do you have the value of $x$, or should I assume a missing proportion to solve for $y$? Let me know!