Answer
16 feet
Work Step by Step
We know that the pitch (the slope) is: $\displaystyle \frac{1}{4}$. If the vertical rise is $4$ feet, we can find the horizontal length:
$slope=\frac{rise}{run}=\frac{4}{x}=\frac{1}{4}$
$\frac{4}{x}=\frac{1}{4}$
$4*4=x$
$x=16$
So the horizontal length must be 16 feet.