You say "I then found the derivative", but is NOT the derivative of . Rather, you should say "I realised that this is a 0/0 indeterminate form, so in order to use L'Hospital's Rule, and evaluated the derivative OF THE NUMERATOR and the derivative OF THE DENOMINATOR and then evaluated the limit."
Also (12x + 5)/(8x + 16) does NOT equal 11/20. But
I'm forgiving, but your lecturer might not be.
Second, you would only ever evaluate the second derivatives of the numerator and denominator (i.e. use L'Hospital's Rule twice) if after using L'Hospital's Rule once, you still get a or indeterminate form. Since after evaluating the derivatives once, you are able to substitute and get a value for the limit, there is no need, and it is completely wrong to, continue with more uses of L'Hospital's Rule.