When two genes from two different people are sequenced and aligned, it is discovered that there are multiple sequence differences in the coding segment DNA level. However, when the proteins formed by the genes have their amino acids sequenced, there is no difference observed between the two. What is the most likely explanation for this observation

On the basis of the phenomenon of the degeneracy of codons, the coding of single amino acid can take place by various codons like four different codons, that is, CCC, CCU, CCG and CCA can code for single amino acid proline.  

In case, if there is a mutation in DNA, due to which CCA get transformed to CCG, even in such case coding for the same amino acid proline will take place. Hence, one can conclude that at the level of DNA mutation is taking place, however, the same is not getting witnessed in a protein, and that is why such kind of mutations are termed as silent mutation.  

i believe it is "they are not used up by reactions" as the answer to your question, text me back if this is correct because i just learned this.