1. **State the problem:** Factorize the expression $6xy - 4y + 6 - 9x$. 2. **Group terms:** Group the terms to find common factors: $$ (6xy - 4y) + (6 - 9x) $$ 3. **Factor out common factors in each group:** - From $6xy - 4y$, factor out $2y$: $$ 2y(3x - 2) $$ - From $6 - 9x$, factor out $3$: $$ 3(2 - 3x) $$ 4. **Rewrite the second group to match the first:** Note that $2 - 3x = -(3x - 2)$, so: $$ 3(2 - 3x) = -3(3x - 2) $$ 5. **Rewrite the expression:** $$ 2y(3x - 2) - 3(3x - 2) $$ 6. **Factor out the common binomial factor $(3x - 2)$:** $$ (3x - 2)(2y - 3) $$ **Final answer:** $$ (3x - 2)(2y - 3) $$