Answer
vertical asymptote $x=0$,
horizontal asymptote $none$,
oblique asymptote $none$.
Work Step by Step
Step 1. Factor the function $F(x)=\frac{x^4-16}{x^2-2x}=\frac{(x^2+4)(x+2)(x-2)}{x(x-2)}=\frac{(x^2+4)(x+2)}{x}, (x\ne2)$,
Step 2. we can find the vertical asymptote $x=0$,
Step 3. we can find the horizontal asymptote $none$,
Step 4. we can find the oblique asymptote $none$.