At the point where you had
limx→33x(x−3)3−x you should simply cancel down to get
limx→33x−1.
From here you should be able to simply finish using the laws you've been given about things like "the limit of a quotient = the quotient of the limits".
Similarly in the 2nd case you can simply rewrite the limit as
limx→−2x+23x+8 and again I would expect the limit laws you have would enable you to finish.
Perhaps the most important thing to realise here is that if you are asked to find
limx→af(x), where f is some complicated function, then you can do whatever simplification you want to f without affecting the limit. This doesn't require any limit laws, since you're not actually changing f, just "writing it in a different way".
If you want more specific help you will need to post exactly
what example 3.2, Theorem 3.6 etc. are.
I don't see how you can possibly use L'Hoptial etc. unless it is one of the named theorems you've been told you can use.