To find the value of \( x \), we can use the given ratio \( \frac{x}{8} = \frac{y}{16} \) and the new value of \( y = 3 \) units.
First, substitute \( y \) into the ratio:
\[ \frac{x}{8} = \frac{3}{16} \]
Next, we'll cross-multiply to solve for \( x \):
\[ x \cdot 16 = 3 \cdot 8 \]
This simplifies to:
\[ 16x = 24 \]
Now, divide both sides by 16 to isolate \( x \):
\[ x = \frac{24}{16} = \frac{3}{2} = 1.5 \]
So, the value of \( x \) is 1.5 units.