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

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Calculate or simplify the expression $$ (2x-3y)^2-(x-y)(3x+2y) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(2x-3y\right)^{2}-\left(x-y\right)\left(3x+2y\right)$$
- step1: Multiply the terms:
  $$\left(2x-3y\right)^{2}+\left(-x+y\right)\left(3x+2y\right)$$
- step2: Expand the expression:
  $$4x^{2}-12xy+9y^{2}+\left(-x+y\right)\left(3x+2y\right)$$
- step3: Expand the expression:
  $$4x^{2}-12xy+9y^{2}-3x^{2}+xy+2y^{2}$$
- step4: Subtract the terms:
  $$x^{2}-11xy+11y^{2}$$
The simplified form of the expression $$ (2x-3y)^{2}-(x-y)(3x+2y) $$ is $$ x^{2}-11xy+11y^{2} $$.
The simplified form is $$ x^{2}-11xy+11y^{2} $$.

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