Let's simplify the expression step by step:

4(3x-2y)^2 - 9(4x+3xy)^2

First, expand the squares:

4(9x^2 - 12xy + 4y^2) - 9(16x^2 + 24xy + 9x^2y^2)

Now distribute the coefficients:

36x^2 - 48xy + 16y^2 - 144x^2 - 216xy - 81x^2y^2

Combine like terms:

(-108x^2 - 264xy - 81x^2y^2)

So, the simplified expression is -108x^2 - 264xy - 81x^2y^2.