To factorize the expression, we can group the terms as follows:
ac - 2bc - a + 4b^2 = a(c - 1) - 2b(c - 2b)
Now we can factor out the common factors:
a(c - 1) - 2b(c - 2b) = (c - 1)(a - 2b)
So the completely factored form of the expression is:
ac - 2bc - a + 4b^2 = (c - 1)(a - 2b)
Therefore, the correct answer is option A: (a - 2b)(c - a - 2b).