How to simplify this? What did I do wrong? $$(3-\sqrt3) (2-\sqrt3)-\sqrt3\cdot\sqrt{27}.$$
So I simplified the $\sqrt3\cdot\sqrt{27}$ part into 
$$\sqrt 3\cdot\sqrt{9\cdot3} = \sqrt3\cdot3\cdot\sqrt3=4\cdot\sqrt3$$
Then I multiplied the brackets :
$$6+\sqrt3-2\cdot\sqrt3-3\cdot\sqrt3 =6-4\cdot\sqrt3.$$
Then minus the $4\cdot\sqrt3$ we got 
$$6-8\cdot\sqrt3$$ 
However the answer should be $-5\cdot\sqrt3$
How can I get that answer, what did I do wrong?

Your mistake was in the equality $$\sqrt 3 \cdot 3 \cdot \sqrt 3 = 4\cdot \sqrt3$$ which is false.
$$\sqrt{3}\sqrt{9\cdot 3} = \sqrt{3}\cdot 3\cdot \sqrt{3} = \sqrt{3}\cdot \sqrt{3} \cdot 3 = 3\cdot 3 = 9 \neq 4\cdot \sqrt 3$$
Also, you made a mistake in multiplying the brackets:
$$(3-\sqrt 3)(2-\sqrt 3) = 6-3\sqrt 3 -2\sqrt 3 + 3$$
which is not what you got.
