To find the equivalent ratio of 12:9 in the form of 4:x, we start with the given ratio 12:9.
First, simplify 12:9:
\[ \frac{12}{9} = \frac{4}{3} \]
Now we need to express 4:x using the simplified ratio 4:3. This means we want 4 to remain the same, so we can set up the proportion:
\[ \frac{4}{3} = \frac{4}{x} \]
To solve for x, we can cross-multiply:
\[ 4 \cdot x = 3 \cdot 4 \]
\[ 4x = 12 \]
Now, divide both sides by 4:
\[ x = 3 \]
Thus, the equivalent ratio of 12:9 in the form of 4:x is:
\[ 4:3 \]
So, the final answer is:
4:3