To find an equivalent ratio for \( 12:9 \) in the form of \( 4:x \), we need to find the value of \( x \).
First, simplify the ratio \( 12:9 \):
\[ \frac{12}{9} = \frac{4}{3} \]
Now set up the equivalent ratio with \( 4:x \):
\[ \frac{4}{3} = \frac{4}{x} \]
Now, we can cross-multiply to solve for \( x \):
\[ 4 \cdot x = 4 \cdot 3 \]
This simplifies to:
\[ 4x = 12 \]
Now, divide both sides by 4:
\[ x = 3 \]
Thus, the equivalent ratio is:
\[ 4:3 \]
So the final answer is \( 4:3 \).