To find an equivalent ratio of 12:9 in the form of 4:x, we can set up a proportion:
\[ \frac{12}{9} = \frac{4}{x} \]
Next, we can cross-multiply:
\[ 12x = 36 \]
Now, solve for \(x\):
\[ x = \frac{36}{12} = 3 \]
Therefore, the equivalent ratio is:
\[ 4:3 \]
So, the answer is 4:3.