To determine the number of inches per foot, we need to simplify the equation \(4y = 48x\) where \(y\) represents feet and \(x\) represents inches.
Starting with the equation:
\[ 4y = 48x \]
We can solve for \(y\) when \(x = 1\) (which signifies 1 inch):
\[ y = \frac{48x}{4} \]
Simplifying this:
\[ y = 12x \]
Now, if \(x = 1\) (which represents 1 inch), substituting this into the equation yields:
\[ y = 12(1) = 12 \]
This means that there are 12 inches in 1 foot.
Thus, the number of inches per foot is \( \boxed{12} \).