Consider $6x^{2}+xy-2y^{2}$ as a polynomial over variable $x$.
$$6x^{2}+yx-2y^{2}$$
Find one factor of the form $kx^{m}+n$, where $kx^{m}$ divides the monomial with the highest power $6x^{2}$ and $n$ divides the constant factor $-2y^{2}$. One such factor is $2x-y$. Factor the polynomial by dividing it by this factor.
