1. **Problem statement:** Find the difference $A - B$ given the equation $$-x^2y + A + 2xy^2 - B = 3x^2y - 4xy^2$$ 2. **Formula and rules:** To find $A - B$, isolate $A - B$ on one side by grouping terms and moving all other terms to the opposite side. 3. **Step-by-step solution:** Start with the given equation: $$-x^2y + A + 2xy^2 - B = 3x^2y - 4xy^2$$ Group $A$ and $-B$ together: $$A - B = 3x^2y - 4xy^2 + x^2y - 2xy^2$$ Simplify the right side by combining like terms: $$3x^2y + x^2y = 4x^2y$$ $$-4xy^2 - 2xy^2 = -6xy^2$$ So, $$A - B = 4x^2y - 6xy^2$$ 4. **Final answer:** $$\boxed{A - B = 4x^2y - 6xy^2}$$ This means the difference $A - B$ equals $4x^2y - 6xy^2$.