step1

given information

the intensity, I, of light received at a source varies inversely as the square of the distance , d, from the source

hence

I= kd^-2  -----------------------------------------------1

where is k is constant  of proportation

step2

the light intensity is 46-ft-candles at 27ft , we RE QUIRES  LIGHT INTENSITY AT  9 ft

from 1 equation

I = kd^-2

I1= kd1^-2  --------------------------------------------3

I2=  k d2^-2--------------------------------------------4

divide  3/4  equation we gets

I1/I2= d1^-2/d2^-2

given data

I1=  46 ft

d1= 27 ft

d2= 9 ft

I2= ?

HENCE 

46/I2=  9^2/27^2

I2=  414 ft