To solve the equation \( y:51.6 = 11.2:34.4 \), we can first rewrite it in a more manageable form. This can be expressed as:
\[ \frac{y}{51.6} = \frac{11.2}{34.4} \]
Next, we can find the value of the right side of the equation:
\[ \frac{11.2}{34.4} \]
Calculating this gives:
\[ \frac{11.2}{34.4} = \frac{11.2 \div 11.2}{34.4 \div 11.2} = \frac{1}{3.07142857} \approx 0.325 \]
Now we can rewrite the equation as:
\[ \frac{y}{51.6} \approx 0.325 \]
To find \( y \), we can multiply both sides of the equation by \( 51.6 \):
\[ y \approx 0.325 \times 51.6 \]
Calculating this gives:
\[ y \approx 16.8 \]
So, the value of \( y \) is approximately 16.8.