the equation is
x^2 - y^2 =12 where y = x-2 .
What are you supposed to do with this? Are you solving a system of equations?
none of the methodology (e.g. factorisation or quadratic formula) in her notes or the text books give me the right answer.
Please show what you did so we can see what's going wrong.
Through factorisation, x = -2 which is wrong
How did you get this by factoring??
Substitution is what they show here
for doing this.
x^2 - (x - 2)^2 = 12
x^2 - (x^2 - 4x + 4) = 12
What did you get from this?