Hello, I hope you are doing well

As per the CBSE Rule, you can only appear in compartment exam if you have failed in 1 subject. If you fail in more than 1 subject, you will be considered fail in that class, there will be no compartment exam for you. You will have to repeat the class.

Also, improvement exam is out of the picture, since it is only for those students who passed the exams but they are not satisficed with their result. So you will have to repeat your Class 12.

Hope this helps.

All the best!