booking an IGCSE exam

hi, I'm currently in year 12 and I want to do one IGCSE exam this summer as I need further maths for the applications. I missed the deadline in school so I would have to book it myself, is that any possible?

It is. It means you'll be sitting Further Maths as a "private candidate".
If you'll be taking other exams at your school this summer, then you won't be able to sit the Further Maths exams in your school, as you can't be both a private candidate and a non-private candidate at the same exam centre for the same exam series. Actually, it sounds like your school might not accept private candidates anyway. So you'll need to find another local exam centre (typically a school or college) to actually sit the exams.
You can use this search tool to find local exam centres which accept private candidates. The exam board will charge you a "very late" entry fee. You probably only have a couple of weeks left before even that option vanishes.
When you book with the exam centre, make sure to check whether they will register you with the exam board too, or whether you need to do that yourself, separately.

omg thank you sm! you are the person that replied on my other thread!!
I looked up the website, but unfortunately there is no school that offer private student to sit a GCSE in my country.
but again, thank you so much for your answer!

If your only option is to sit the exam at your school, and if you've missed the application deadline, then you might be out-of-luck. Your school can still register you, but they'll have to pay a "very late registration" fee. If you offer to cover that cost, they might be willing to register you.
Also, as you're in Year 12, you may not be taking any other exams this summer anyway (are you?), in which case you may be able to register with the exam board as a private candidate and specify your current school as your exam centre. Your school would need to be happy to accept this arrangement, however.
Have you spoken to your school about either of the above options? If there are no schools in your country which accept private candidates, then any solution has to involve your current school.