Key idea. Remove the common factor first, then factor the remaining quadratic.

1. Every term contains \(3xy\):

   \[6x^3y-9x^2y^2+3xy^3=3xy(2x^2-3xy+y^2).\]

2. To factor the bracket, split its middle term:

   \[2x^2-3xy+y^2=2x^2-2xy-xy+y^2.\]

3. Group and factor:

   \[2x(x-y)-y(x-y)=(2x-y)(x-y).\]

4. Restore the common factor \(3xy\). The complete factorisation is \(3xy(2x-y)(x-y)\).

Remember. Factoring can take more than one step. Do not stop after taking out the common factor.