Let's simplify the expression step by step. The given expression is:

\[
(x - 3) - 2x + 6x \cdot (x - 3) - 2x + 6
\]

First, we'll group and simplify terms. Let's break it down into smaller parts:

1. Identify the individual components:
- The first part: \((x - 3)\)
- The second part: \(-2x\)
- The third part: \(6x \cdot (x - 3)\)
- The fourth part: \(-2x\)
- The fifth part: \(+6\)

2. We'll start by simplifying \(6x \cdot (x - 3)\):
\[
6x(x - 3) = 6x^2 - 18x
\]

3. Now, let's rewrite the original expression with this result:
\[
(x - 3) - 2x + (6x^2 - 18x) - 2x + 6
\]

4. Next, let's combine like terms. Start with \(x\) terms:
\[
(1 - 2 - 18 - 2)x = (-21)x
\]
and then constants:
\[
(-3 + 6) = 3
\]

5. The expression now looks like this:
\[
6x^2 - 21x + 3
\]

Thus, the simplified expression is:

\[
\boxed{6x^2 - 21x + 3}
\]