\(6xy\left(\dfrac{1}{2}x^2y-\dfrac{1}{3}x^3y^2-1\right)\)
\(=6xy\cdot\dfrac{1}{2}x^2y+6xy\cdot\left(-\dfrac{1}{3}x^3y^2\right)+6xy\cdot\left(-1\right)\)
\(=3x^3y^2-2x^4y^3-6xy\)
\(6xy\left(\dfrac{1}{2x^2y}-\dfrac{1}{3x^3y^2}-1\right)\)
\(=\dfrac{3}{x}-\dfrac{2}{x^2y}-6xy\)