how can a mutaion affect protein synthesis by a cell? Do you think there are different consequence if it happens in a gamete cell (sperm or egg) versus a non-gamate cell?

A mutation alters the sequence of DNA. Therefore, the mRNA that is transcribed from the DNA has a different sequence.

This mRNA goes on to be read by the protein synthesis machinery in the cell. The protein synthesis machinery translates the sequence of the mRNA into an amino acid sequence, which makes up the protein.

If the sequence of the mRNA is different, due to a mutation in the DNA, then the cell will translate a different sequence into an amino acid. This alters the composition of the protein.

Mutations can be small, and affect only one amino acid, or they could be huge, and impact the entire protein.

Mutations have very different consequences in gametes vs non-gamete cells.

If a mutation occurs in a gamete, that means the mutation will be passed on to the next generation, as it is contained in the DNA in the egg or sperm that becomes fertilised to make a gamete.

However, mutations that occur in other cells are not passed on to the next generation. That does not mean they do not have effects. E. g. mutations in the skin caused by exposure to UV rays from the sun can contribute to cancer, but would not be passed on to the individual's children