Meiosis reduces the chromosome count by half. Mitosis does not effect the chromosome count of the next cellular generation. I think that the question is really concerned with ensuring that you understand this difference. You are correct that cells produced by mitosis can produce gametes through meiosis. However, if you think of reproduction in plants, for example, where haploid spore cells (products of meiosis) undergo several rounds of mitosis and differentiate into both gametes and somatic cells (the gametophytic generation), you will find that haploid meiotic products can and do differentiate into gametes. I think that you could be confused by the difference between the processes of DNA transfer between generations of cells (I mean both mitosis and meiosis collectively under this definition) and the process of cellular differentiation where cells (either diploid or haploid) will differentiate to fulfill some role. This all being said, it's not really meiosis that "produces" gametes, meiosis is just a cellular process that reduces chromosome count by half, the process of differentiation which is independent from meiosis and mitosis is the driving factor behind what the cell turns into. So this is why I wouldn't choose E, cells produced by meiosis commonly do differentiate into gametes, but I agree with you that this multiple choice option is worded confusingly. Does this make sense?