To simplify this expression, we first need to expand and simplify the terms.

First step:
3(1-4b)^2 expands to 3(1-8b+16b^2)
= 3(1-8b+16b^2)
= 3 - 24b + 48b^2

Second step:
-3(4b+1)(1-4b) expands to -3(4b+1-16b)
= -3(4b+1-16b)
= -12b - 3 + 48b
= 36b - 3

Now we need subtract the result of the second step from the result of the first step:

(3 - 24b + 48b^2) - (36b - 3)
= 3 - 24b + 48b^2 - 36b + 3
= 48b^2 - 60b + 6

Therefore, the simplified expression is 48b^2 - 60b + 6.