To simplify the expression \((x-2)(x-3) - (x-4)^2\), we need to expand both parts and then combine like terms.

First, let's expand \((x-2)(x-3)\):

\[
(x-2)(x-3) = x(x-3) - 2(x-3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6
\]

Next, let's expand \((x-4)^2\):

\[
(x-4)^2 = (x-4)(x-4) = x(x-4) - 4(x-4) = x^2 - 4x - 4x + 16 = x^2 - 8x + 16
\]

Now, we subtract the second expanded expression from the first:

\[
(x^2 - 5x + 6) - (x^2 - 8x + 16)
\]

Distribute the negative sign through the second polynomial:

\[
x^2 - 5x + 6 - x^2 + 8x - 16
\]

Combine like terms:

\[
(x^2 - x^2) + (-5x + 8x) + (6 - 16) = 0 + 3x - 10 = 3x - 10
\]

So, the simplified form of the expression \((x-2)(x-3) - (x-4)^2\) is:

\[
\boxed{3x - 10}
\]