1. ((d + 2)/(d + 8)) = ((-6)/(d + 8))
A: ?
2. 4/n^2 = 7/n + 2
A: n = -4 or n = 1/2?
3. 2/t + 4/3t = 4/t + 2
A: t = 10?
4. ((x -6)/(x^2-6)) = ((-4)/(x-4))
A: ?
#1 no solution
#2 ok
#3 ok
but I had to try two different ways of inserting parentheses before I got your answer. Grrr. The spacing in "t + 2" was especially deceptive.
#4 x = 0 or 2
This time, overkill. Use parens as needed, but only as many as it takes to avoid ambiguity. I'd have said
(x -6)/(x^2-6) = (-4)/(x-4)