\[x^{2} + xy - 6y^{2} =\]
\[= x^{2} + xy + 0,25y^{2} - 6,25y^{2} =\]
\[= (x + 0,5y)^{2} - 6,25y^{2} =\]
\[= (x - 2y)(x + 3y).\]