I recently received my Non-Immigration visa Class "B" but my family members received class "O" with "Extension of stay not permitted." I understand that mine will be converted to "work permit", but I still don't understand why my family members are not permitted to extend their stay with me? Anybody can explain? Thanks.

Once you have a 12 month extension your family will be able to get 12 month extensions as your dependents.

You will not be converted to a work permit, rather you will also recieve a work permit. This work permit allows you to work.

Don't read too much into the "extension of stay not permitted" stamp, they can get extensions of stay just like you. But for them to get an extension of stay, you must first get an extension of stay as their stay will be tied to yours. If you are no longer allowed to stay, they also have to leave.

If your children go to school, they can get their own extensions of stay based on their education.

That stamp is just to alert you that the normal 30 day extension provided on a tourist visa entry is not available on a non immigrant visa entry. Authorized Police Order 777/2551 extensions of stay are available.

Thanks to all who gave information regarding my querry. By the way, how long does it normally take to get a work permit with my non-immigration class "B" visa?

That depends on the job, the employer and the labour office where you will be applying. It can take up to a few weeks.