how do you find the axis intercepts and asymptotes
f(x)=(3x^2-2x)/(x^2-4)
... y-intercept
at and at x = \frac{2}{3} ... x-intercepts
vertical asymptote, and x = 2 ... in the denominator
horizontal asymptote at ... degree of the numerator = degree of the denominator ... ratio of the leading coefficients in the numerator and denominator gives you the value of the horizontal asymptote.
To learn the general rules, study some online lessons on asymptotes and intercepts. Then please return here and review the solutions you were provided for this particular exercise, and confirm that you understand the concepts and methods they used.