To solve the proportion \( 4.9 : 0.6 = X : 2.4 \), we can set up the equation as follows:
\[ \frac{4.9}{0.6} = \frac{X}{2.4} \]
Next, we can cross-multiply:
\[ 4.9 \cdot 2.4 = 0.6 \cdot X \]
Calculating the left side:
\[ 4.9 \cdot 2.4 = 11.76 \]
Now we have:
\[ 11.76 = 0.6 \cdot X \]
To solve for \( X \), divide both sides by \( 0.6 \):
\[ X = \frac{11.76}{0.6} \]
Calculating this gives:
\[ X = 19.6 \]
So, the answer is:
\[ X = 19.6 \]