To solve the ratio given by Ethan, we have:
\[ \frac{x}{8} = \frac{y}{16} \]
We know that the new value of \( y \) is 3 units, so we substitute \( y \) with 3:
\[ \frac{x}{8} = \frac{3}{16} \]
Now, to find the value of \( x \), we can cross-multiply:
\[ x \cdot 16 = 3 \cdot 8 \]
Calculating the right side:
\[ x \cdot 16 = 24 \]
Now, solve for \( x \) by dividing both sides by 16:
\[ x = \frac{24}{16} = \frac{3}{2} = 1.5 \]
Therefore, the value of \( x \) is:
\[ 1.5 \text{ units} \]
So the final answer is:
1.5 units.