To solve for \( x \) in the ratio \( \frac{x}{8} = \frac{y}{16} \) with the given value of \( y = 3 \), we can start by substituting \( y \) into the equation:
\[ \frac{x}{8} = \frac{3}{16} \]
Next, we will cross-multiply to solve for \( x \):
\[ 16x = 3 \times 8 \]
Calculating the right side:
\[ 16x = 24 \]
Now, we divide both sides by 16 to find \( x \):
\[ x = \frac{24}{16} = \frac{3}{2} = 1.5 \]
Thus, the value of \( x \) is \( \boxed{1.5} \) units.