To determine the number of centimeters in 1 inch from the equation \(6y = 15.24x\), we can interpret \(y\) as the number of centimeters in 1 inch and \(x\) as the number of inches.
We can rewrite the equation to isolate \(y\):
\[ y = \frac{15.24}{6}x \]
Now, if we are looking for the value of \(y\) when \(x = 1\):
\[ y = \frac{15.24}{6} \cdot 1 = \frac{15.24}{6} \]
Calculating this gives:
\[ y = 2.54 \]
Thus, the number of centimeters in 1 inch is \( \boxed{2.54} \) centimeters.