all the teachers discussed the plan that they would like to see[ ] in the next year.

plan 是被实施的

这个句子是个复合句。其中“that they would like to see carried out in the next year”是定语从句，属于“the plan”的定语。如果把定语从句转换为一个完整的句子，那就是：“They would like to see the plan carried out in the next year.”(see+sth+done,看到某事物被...)the plan在定语从句中属于被动，所以填carried out.