I am 11 and half years old, and I would like to know how many mishayos a day I have to learn in order to finish the who shisha sidrei mishna by my bar mitzva?
There is an excellent website here that will generate charts for you based on the amount of mishnas you want to learn each day.
Based on the fact that you are eleven and a half you will need to finish it in a year and a half. There are 4192 mishnas divide it by the amount of days it is to your bar mitzva you will be able to determine how many mishnas you have to do. For example, if it's 530 days to your Bar-Mitzvah divide 4192 by 530 and it's about 8 mishnas a day to finish in time. Hatzlacha on learning and finishing.
My son and I did this. Figure roughly 12 per day to finish in one year. It's a lot, but it's doable in a year and a half.
Here is a tracker you can use to help you. Enter the date of the Bar Mitzvah at the bottom, and it will calculate how many Mishnayoth you have to learn per day to meet your goal.
Some tips: We fell significantly behind at one point, and we ended up finding clever ways to catch up. For example, during Sefirah last year, we learned a Perek of Pirkei Avoth each week, Shabbath afternoon, and did not count that towards our day's Mishanayoth, so if the tracker said we needed to learn 7.32951 Mishnayoth per day (for example), we would learn 8 Mishnayoth plus the Perek. We picked Pirkei Avoth because a lot of it is not very complicated, and there are many good translations available out there. We used Artscroll's Children's Pirkei Avos and a standard, Artscroll Hebrew-English Siddur. In general we used Sefaria.org for our learning, which made it easier, but of course on Shabbath we couldn't. For a few Masechtoth we used translated Mishnayoth, but most weeks we either used Kehati or waited until Saturday night to get online to use Sefaria.
Kol HaKavod for taking this on, and Hatzlachah Rabbah in completing it.
Incidentally, the Agudah has a program in which you can take tests on the material, and they have a celebration together (I'm not sure if it's a Siyum when you finish, or if it's at a set time each year for each cohort). The boys who participate celebrate with their fathers and grandfathers, as it was explained to me, and they receive a set of Mishnayoth. We learned of it after the fact, but it's worth calling and asking about if it's something you are interested in doing. Their main number is 212.797.9000.