All you need to do is subtract the expressions of the two functions:
[tex](f-g)(x) := f(x)-g(x)[/tex]
So, in your case, we have
[tex](f-g)(x) := f(x)-g(x) = 3x^2-2x+4 - (5x^2+6x-8) = -2x^2-8x+12[/tex]
