2a - [4b - {4a - (3b - 2a + 2b)}]

We remove the vinculum which causes the "+ 2b" to become "- 2b":

2a - [4b - {4a - (3b - 2a - 2b)}] 

We combine like terms inside the parentheses:

2a - [4b - {4a - (b - 2a)}]

We remove the parentheses, causing the "- 2a" to become "+ 2a"

2a - [4b - {4a - b + 2a}]

We combine like terms inside the braces:

2a - [4b - {6a - b}]

We remove the braces, causing the "- b" to become "+ b"

2a - [4b - 6a + b]

We combine like terms inside the brackets:

2a - [5b - 6a]

We remove the brackets, causing the "- 6a" to become "+ 6a":

2a - 5b + 6a

We combine like terms:

8a - 5b

Edwin