how would you solve this problem?

A = -8

Cross multiply the factions
(x^2(x-A)-x^2(x+6))/((x+6)(x-A))
expand
((-A-6)x^2)/(x^2+(6-A)x-6A)

so if we only worry about the highest power on each fraction we get
(-6-A)x^2/x^2 = 2
(-6-A)x^2 = 2x^2
-6-A = 2
A = -8

Let me know if you have any questions