1. **State the problem:** Fully factorise the expression $6x + 18y + 24z$. 2. **Identify the greatest common factor (GCF):** Look for the largest number that divides all coefficients 6, 18, and 24. 3. The GCF of 6, 18, and 24 is $6$ because: $$6 = 6 \times 1$$ $$18 = 6 \times 3$$ $$24 = 6 \times 4$$ 4. **Factor out the GCF:** $$6x + 18y + 24z = 6(x) + 6(3y) + 6(4z)$$ 5. Use the distributive property to factor out 6: $$= 6(x + 3y + 4z)$$ 6. **Final answer:** $$\boxed{6(x + 3y + 4z)}$$ This is the fully factorised form because the expression inside the parentheses has no common factors.