I need to factor
$\displaystyle 6x^2+xy-2y^2$
I don't know what to do with this
This looks difficult, but try to think of it as a normal quadratic, just ignore the $\displaystyle y$ for the moment, we then get $\displaystyle 6x^2+x-2$.
I'm sure you can factorise this to get $\displaystyle (3x+2)(2x-1)$.
If we put the $\displaystyle y$ back in, we then get $\displaystyle (3x+2y)(2x-y)$.
Multiply that out, what do you get?
Hope this helps