The genetic code and the effect of point mutations on proteins
Nonambiguity refers to the fact that codon X will always code for the same amino acid.

Degeneracy refers to the fact that an amino acid can be coded for by many codons. 

I rephrase the question to get to the gist of things:


  Why do certain mutations cause no difference for protein synthesis, while others make a big difference?


Certain mutations can change the codon but still code for the same amino acid, so the resulting peptide sequence is unaltered (synthesis of a functionally identical protein). This is due to degeneracy, explained above. Certain other mutations change the codon in a way that produces a completely different amino acid, and these result in the synthesis of a different, distinct peptide that may be dysfunctional. This due to nonambiguity of the code. Simple!

It's best to refer to our translation guide, the codon table. If you know your codon table, you might have noticed that within a codon frame, changing the 3rd nucleotide often has no effect on the translated amino acid (see outer ring, below). Changing the 1st and 2nd nucleotide produces a more drastic effect in the translation of the codon. 

That means that the position of a nucleotide mutation within the reading frame is key to the effect of the mutation on protein synthesis.




  Where I am going wrong?


You are complicating the picture needlessly. You fail to explain that the resulting amino acid depends on its codon, and that the effect of changing the codon in different places (position 1, 2 or 3) has different outcomes. You also have to think about different kinds of mutations; we are discussing substitutions, but you must also consider what deletions and insertions of nucleotides do to the translation of the peptide! You may also get bonus points for discussing the start and stop codons... they are special cases.