First, let's simplify the expression step by step:

Expand the first term using the distributive property:
(2a-b)(a+b) = 2a^2 + 2ab - ab - b^2
= 2a^2 + ab - b^2

Expand the second term using the distributive property:
-3(4c-1)^2 = -3(16c^2 - 8c + 1)
= -48c^2 + 24c - 3

Now, substitute the expanded forms back into the original expression:
(2a^2 + ab - b^2) - (48c^2 - 24c + 3)
= 2a^2 + ab - b^2 - 48c^2 + 24c - 3

Therefore, the simplified form of the expression is:
2a^2 + ab - b^2 - 48c^2 + 24c - 3