To solve the proportion \( y : 51.6 = 11.3 : 34.4 \), we can use cross multiplication. This means we can set up the equation as follows:
\[ y \cdot 34.4 = 51.6 \cdot 11.3 \]
Now, let's calculate \( 51.6 \cdot 11.3 \):
\[ 51.6 \cdot 11.3 = 583.08 \]
Now, we substitute this back into the equation:
\[ y \cdot 34.4 = 583.08 \]
Next, solve for \( y \):
\[ y = \frac{583.08}{34.4} \]
Now, let's perform the division:
\[ y \approx 16.95 \]
Thus, the value of \( y \) is approximately \( 16.95 \).