I'm not a teacher, but here is my take on it.
Your meaning is unclear here.
If you ordered him to do it and it wasn't done,
the passive is sort of understood here, I would think.
What I ordered him to do should have been done. (by him)
if some other action occurred with the order, you should expand on that in the sentence.
What I ordered him to do should have been done by him, instead of by X, being cancelled, etc.
Student or Learner