6. \( (2 x-3 y)^{2}-(x-y)(3 x+2 y) \)

To solve the expression \( (2 x-3 y)^{2}-(x-y)(3 x+2 y) \), let's start by expanding each part. First, expand \( (2x - 3y)^{2} \): \[ (2x - 3y)^{2} = 4x^{2} - 12xy + 9y^{2}. \] Next, we will expand the term \( (x - y)(3x + 2y) \): \[ (x - y)(3x + 2y) = 3x^{2} + 2xy - 3xy - 2y^{2} = 3x^{2} - xy - 2y^{2}. \] Now, putting it all together: \[ (2x - 3y)^{2} - (x - y)(3x + 2y) = (4x^{2} - 12xy + 9y^{2}) - (3x^{2} - xy - 2y^{2}). \] Distributing the negative sign: \[ 4x^{2} - 12xy + 9y^{2} - 3x^{2} + xy + 2y^{2}. \] Now, combine like terms: \[ (4x^{2} - 3x^{2}) + (-12xy + xy) + (9y^{2} + 2y^{2}) = x^{2} - 11xy + 11y^{2}. \] Therefore, the simplified expression is: \[ \boxed{x^{2} - 11xy + 11y^{2}}. \]