1. **State the problem:** Fully factorise the expression $$18x^2 + 12xy - 24x$$. 2. **Identify the greatest common factor (GCF):** Look at the coefficients 18, 12, and -24. The GCF of these numbers is 6. Also, each term contains at least one factor of $$x$$. 3. **Factor out the GCF:** Extract $$6x$$ from each term: $$18x^2 + 12xy - 24x = 6x(3x) + 6x(2y) - 6x(4) = 6x(3x + 2y - 4)$$ 4. **Check if the expression inside the parentheses can be factored further:** The trinomial $$3x + 2y - 4$$ has no common factors and is not factorable further with respect to $$x$$ and $$y$$. 5. **Final answer:** The fully factorised form is: $$6x(3x + 2y - 4)$$