If her Mother says No, then that means No ! You'll both get into trouble without her permission. I suggest you spend some time getting to know her parents better and maybe they will lighten up and let her go to a movie or something with you. It's up to you to show them that you're a good respectable young man. Give it a try!
My girlfriend's Mom said she can't date, what should she do? Listen to her mom or obey them? Means I get into trouble without asking her mother? Is that good or not?
If your name is truly Takahashi your lineage is from a nation that respects parents and elders. You can expect your girlfriend to do no less.
My thought was the same as Rooster's. Get to know her parents. Establish yourself as somebody they can trust.
Yes, you should ask for the permission of your girlfriend's mother. If she doesn't agree with your dating, you'd better talk with her sincerely, and make her mother know you love her daughter. It may take much time, but don't give up! Good Luck!
Encourage your friend to listen to her parents. We may sometimes reason that our parents are not cool or that they don't understand how we feel. But that is simply not the case. They are much more experienced that you give them credit for. The bible states reasons that you just can't ignore. Ephesians 6:1-3 tells us "Children, be obedient to your parents, in union with the lord because this is righteous. Honor your father and your mother.....that it may go well with you and you may remain a long time on the earth". Your time to date will come, so be patient. Her mom isn't trying to stop her fun she is doing her job, looking out for her best interest and protecting her.
You said "Listen to her mom or obey them?" Umm.. "obey" whom? The person they need need to listen to, is her parents, if they say no, then it's no, and if they say no until she is 18, then it is no. If she still lives at home after she is 18, and they say no, then she needs to move out.