Solve for x in the denominator by setting it to zero:
(x+6) = 6
x = -6
Now using the given equation but replace the constant with c :
x^2 +8x +C
Replace x with -6:
(-6)^2 +8(-6) +c
36 - 48 +C = 0
-12 +c = 0
c = 12
The constant needs to be 12 in order for (x+6) to be a factor.