Let's simplify the expression step by step:

4a(a-2) - (a+4)(2a-5) - 20

First, distribute 4a into the expression within the parentheses:

4a^2 - 8a - (a+4)(2a-5) - 20

Then, distribute the values in the second set of parentheses:

4a^2 - 8a - (2a^2 - 5a + 8a - 20) - 20

Now simplify by combining like terms:

4a^2 - 8a - 2a^2 + 5a - 8a + 20 - 20

Combining like terms:

2a^2 - 8a + 20 - 20

Finally, simplify the constant terms:

2a^2 - 8a

Therefore, the simplified expression is 2a^2 - 8a.