To solve the proportion \( 4.5 : 0.6 = x : 2.4 \), you can set it up as a fraction:
\[ \frac{4.5}{0.6} = \frac{x}{2.4} \]
Now, you can cross-multiply to find \( x \):
\[ 4.5 \cdot 2.4 = 0.6 \cdot x \]
Calculating \( 4.5 \cdot 2.4 \):
\[ 4.5 \cdot 2.4 = 10.8 \]
Now the equation becomes:
\[ 10.8 = 0.6x \]
Now, solve for \( x \) by dividing both sides by 0.6:
\[ x = \frac{10.8}{0.6} \]
Calculating \( \frac{10.8}{0.6} \):
\[ x = 18 \]
So, the value of \( x \) is \( 18 \).