Can I apply for the teacher recruitment exam if I fail in Putonghua Grade B?

It depends on which direction you are a teacher. Without this certificate, the recruiter will generally not accept you.

According to the regulations of teachers' profession, the requirements for reaching the standard of Putonghua are as follows:

The Putonghua level of teachers in primary and secondary schools, kindergartens and off-campus education units is not lower than Grade II, among which Chinese teachers are not lower than Grade 2A and Putonghua phonetic teachers are not lower than Grade I; The putonghua level of teachers in colleges and universities is not lower than Grade III A, among which modern Chinese teachers are not lower than Grade II A, and Putonghua phonetic teachers are not lower than Grade I A; The Putonghua level of teachers of Chinese as a foreign language should be no less than Grade 2.

Those who apply for the qualification of teachers in primary and secondary schools and kindergartens shall have a level of Putonghua of not less than two.