1. **State the problem:** Simplify the expression $\left(4\sqrt{5}-3\right)\left(\sqrt{5}-2\right)$.\n\n2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in the second parenthesis.\n$$\left(4\sqrt{5}-3\right)\left(\sqrt{5}-2\right) = 4\sqrt{5} \cdot \sqrt{5} + 4\sqrt{5} \cdot (-2) - 3 \cdot \sqrt{5} - 3 \cdot (-2)$$\n\n3. **Calculate each product:**\n- $4\sqrt{5} \cdot \sqrt{5} = 4 \times 5 = 20$ because $\sqrt{5} \times \sqrt{5} = 5$.\n- $4\sqrt{5} \cdot (-2) = -8\sqrt{5}$.\n- $-3 \cdot \sqrt{5} = -3\sqrt{5}$.\n- $-3 \cdot (-2) = 6$.\n\n4. **Combine all terms:**\n$$20 - 8\sqrt{5} - 3\sqrt{5} + 6$$\n\n5. **Combine like terms:**\n$$20 + 6 - (8\sqrt{5} + 3\sqrt{5}) = 26 - 11\sqrt{5}$$\n\n**Final answer:** $$\boxed{26 - 11\sqrt{5}}$$