What values make the inequality x+6/6-x true?

The correct question is
What values make the inequality (x+6)/(6-x)<0 true?

we know that

the denominator cannot be zero;
so
(6-x)> will be  0 if  x=6

the inequality is true
when
(x+6) > 0  and (6-x) < 0> case 1
or
(x+6) < 0  and (6-x) > 0> case 2

case 1
(x+6) > 0  and (6-x) < 0
(x+6) > 0  > x> -6
(6-x) < 0 > x>  6
 solution> (6,∞)

case 2
(x+6) < 0  and (6-x) > 0
(x+6) < 0  > x< -6
(6-x) > 0 > x < 6
 solution> (-∞,-6)
 
the answer is
the values that makes  the inequality true are
(-∞,-6) ∩ (6,∞)

It would be 18 cm