To find the number that makes the ratio \( 4:x \) equivalent to \( 1:8 \), we can set up the equation based on the equality of the ratios:
\[ \frac{4}{x} = \frac{1}{8} \]
Now, we can cross-multiply to solve for \( x \):
\[ 4 \cdot 8 = 1 \cdot x \]
This simplifies to:
\[ 32 = x \]
So the number that makes the ratio equivalent to \( 1:8 \) is \( 32 \). Thus,
\[ 4:32 \text{ is equivalent to } 1:8. \]