jmc

We see that $$f(4)=(4-1)(4-3)(4-7)(4-9)=(3)(1)(-3)(-5)$$$$f(6)=(6-1)(6-3)(6-7)(6-9)=(5)(3)(-1)(-3).$$But then $f(4)=f(6)$, so $f(6)-f(4)=\boxed{0}$.