The child went to Bai Jiao Primary School, public school and Hung-chien Middle School in Xiaoshengchu, but she was not admitted. Isn't it a nine-year term now?

Now it must be nine-year compulsory education, of course, referring to public schools. If Hung-chien Middle School is a public school and you are in the school district, you should have no problem attending this school. If Hung-chien Middle School is a private school, there will be certain conditions for attending the school, such as entrance examination and so on. You have to find out where your child's current student status is and whether your own conditions meet the requirements of attending Hung-chien Middle School. You can consult the local education authorities for details.