+16 
I got 2(x-2)/(x+2)(x-4) but when I plugged it in, it wasn't the same graph.
The characteristics I got were
VA: x=-2,4
HA: y=0
x int: 2
y int: 1/2
+118608 You are on the right track
Certainly a part of the denominator must be (x+2)(x-4)
And given that (2,0) is on the graph, the numerator must have (x-2) in it.
Plus it looks a bit like a parabola, with a double root at x=2 so i suspect the numerator will be squared (I am not so sure that my logic is sound here)
Anyway so far I am thinking that it might be ..
\(y=\frac{k(x-2)^2}{(x+2)(x-4)}\\\) where k is a constant.
It looks like it might go through (0, 0.4)
when x=0
LHS= 4k / -8 = -k/2
-k/2=0.4
k=-0.8
So maybe it is
\(y=\frac{-0.8(x-2)^2}{(x+2)(x-4)}\\\)
check:
This is certainly not completely correct but the diagram you have provided is not very good.
This is probably close enough.
Maybe -1 would have looked a little closer than -0.8 . The the y intercept would have been 0.5
