What happens when a cell's proteins do not detect a mutation?
a. the mutation leaves the cell before cell division
b. the mutation remains with the cell and is passed on in division
c. the protein is psubstituted with a mutation
d. the mutation becomes part of the protein

The answer is b. the mutation remains with the cell and is passed on in division.

Mutations occur on DNA molecules, so the mutation cannot become part of the protein nor the protein can be substituted with a mutation. Once a mutation happens it remains with the cell unless it is detected by cellular mechanism and fixed. If cell does not detect the mutation, it will not be fixed and the mutation will remain forever with the cell. In the normal process of mitosis (cell division), it will be passed down to the next generation of cells. 

If you want the answer you need to post the figure above that it's talking about and you

If the experiment was perfomed more then once and you get the same results