Alright I'm really confused on this one...

how do you factor

y2(squared)+8

the entire problem is this

y2(squared)+8
F(y)= ----------------
y2(squared)-3y-4

Im looking for the domain.

2. $y^2+8$ will not factor over the real numbers.

the denominator, however, will factor, and once done you should be able to "see" the values that need to be excluded from the domain.