When using the inspection method, which number would you add to (and subtract from) the constant term of the numerator in this expression so the polynomial in the numerator will have (x 4) as a factor?

To be able to factor x + 4 from the last two terms, you need the unit coefficient to be 4 x 18 = 72, so you need to add and subtract 68: 
(x + 4)x + 18x + 4 + 68 - 68 
(x + 4)x + 18x + 72 - 68 
(x + 4)x + (x + 4)18 - 68 

So you end up with: 
(x + 4)(x + 18) - 68 

 
Add and subtract 68

9.8? i'm not really sure