Qual é a diferença entre I must teach him e I should have to teach him ?Você pode indicar exemplo de resposta.

You can say:
"I should teach him". "Should" is used for something which is right, but that you have a choice about. e.g.
"He finds Maths really hard, I should teach him". It's not an obligation, but you feel that teaching him would be the right thing to do.

Or:

"He doesn't understand science, I need to teach him" or "He doesn't understand science, he needs me to teach him." "Need to" normally means circumstances cause you to require something e.g. "I'm hungry, I need to eat/I need food."

"I must teach him well" or "I have to teach him well" is for something you are obliged to do, as mayura9 has said. "have to" is most commonly used nowadays. e.g. "He can't do his homework, I have to help him." or "I can't go tonight, I have to tidy the garage."

And then mayura9's example above for expressing something you regret not doing.

I hope this helps!