To determine the number of centimeters in 1 inch from the proportional relationship given in the equation \(6y = 15.24x\), we can first express the equation in terms of \(y\) (centimeters) and \(x\) (inches).
Rearranging the equation:
\[ y = \frac{15.24}{6} x \]
Now, calculating \(\frac{15.24}{6}\):
\[ \frac{15.24}{6} = 2.54 \]
Thus, the equation simplifies to:
\[ y = 2.54x \]
This shows that for every 1 inch (where \(x = 1\)), the value of \(y\) (in centimeters) is 2.54.
Therefore, the number of centimeters in 1 inch is:
2.54 centimeters.
So the correct response is:
2.54 centimeters.