To find the value of \( x \) given the ratio \( \frac{x}{8} = \frac{y}{16} \) and \( y = 3 \), we start by substituting \( y \) into the equation:
\[ \frac{x}{8} = \frac{3}{16} \]
Next, we can solve for \( x \) by cross-multiplying:
\[ x \cdot 16 = 3 \cdot 8 \]
Calculating \( 3 \cdot 8 \):
\[ 3 \cdot 8 = 24 \]
So we have:
\[ 16x = 24 \]
Now, divide both sides by 16 to isolate \( x \):
\[ x = \frac{24}{16} \]
Now simplify \( \frac{24}{16} \):
\[ x = \frac{24 \div 8}{16 \div 8} = \frac{3}{2} \]
Thus, the value of \( x \) is
\[ \boxed{\frac{3}{2}} \]