To solve for \( x \) in the equation \( \frac{x}{8} = \frac{y}{16} \), we can first substitute \( y \) with the given value of 3 units.
Thus, we have:
\[ \frac{x}{8} = \frac{3}{16} \]
Next, we can cross-multiply to eliminate the fractions:
\[ 16x = 3 \cdot 8 \]
Calculating the right side, we have:
\[ 16x = 24 \]
Now, to find \( x \), we divide both sides by 16:
\[ x = \frac{24}{16} \]
This fraction reduces to:
\[ x = \frac{3}{2} \]
This is equal to 1.5 units. Therefore, the value of \( x \) is:
\[ \boxed{1.5} \text{ units} \]
The correct answer is C. 1.5 units.