Rearrange the equation into standard form:
x+4y-24=0
bring y over to the other side
x-24=-4y
divide both sides by -4

We see that the y-intercept is (0,6) (through y=mx+b)
The formula for perpendicular lines is

, and they must have a common coordinate (this will be (0,6), the y-intercept).
-1÷-x/4=4x, so the slope of the second line will be 4x. The y-intercept doesn't change as the lines share a common coordinate, so the final equation of the second equation is y+4x+6