You need to say what you do and do not understand about this situation.

There are two expressions in the expression illumination (distance)/illumination(2*distance).

One is

illumintation(distance)

and the other is

illumination (2 * distance).

You are given that

illumination (distance) = 50 / distance^2.

From this it follows that

illumination (2 * distance) = 50 / (2 * distance)^2.

So

illumination (distance)/illumination(2*distance) = ( 50 / distance^2 ) / (50 / (2 * distance)^2 ).

(a / b) / ( c / d) = (a / b) * ( d / c), so

( 50 / distance^2 ) / (50 / (2 * distance)^2 ) = ( 50 / distance^2 ) * (2 * distance)^2 / 50.

50 / 50 = 1 so the expression is

(2 * distance)^2 / distance^2, which is equal to

2^2 * distance^2 / distance^2. Since distance^2 / distance^2 = 1, the final result is just

2^2, or 4.