4c(c-2) - (c-4)^2

First, we need to expand the squared term:

(c-4)^2 = (c-4)(c-4)
(c-4)(c-4) = (c^2 - 4c - 4c + 16)
(c^2 - 8c + 16)

Now substitute this back into the original expression:

4c(c-2) - (c^2 - 8c + 16)

Now distribute the 4c:

4c^2 - 8c - c^2 + 8c - 16

Combine like terms:

3c^2 + 0c - 16

Finally, the simplified expression is:

3c^2 - 16.