1. **State the problem:** Fully factorise the expression $8p + 12$. 2. **Identify the common factor:** Both terms $8p$ and $12$ have a common factor of $4$. 3. **Use the distributive property:** The distributive property states that $a(b + c) = ab + ac$. We can factor out the common factor $4$: $$8p + 12 = 4 \times 2p + 4 \times 3$$ 4. **Write the factored form:** Using the distributive property in reverse: $$8p + 12 = 4(2p + 3)$$ 5. **Check if further factorisation is possible:** The expression inside the parentheses, $2p + 3$, cannot be factored further since $2p$ and $3$ have no common factors. **Final answer:** $$8p + 12 = 4(2p + 3)$$