English Grammar: studying versus to study.
"how many hours a day do you take studying your English"?.
"how many hours a day do you take to study your English"?.

"how many hours a day do you spend studying your English"?
"how many hours a day do you spend to study your English"?.

Which of them is more grammatically correct?.

I have a British English Grammar book that taught me that it is wrong to use "to study" but my another English Grammar book taught me that it is not. So I am really confused.

Question

English Grammar: studying versus to study.
"how many hours a day do you take studying your English"?.
"how many hours a day do you take to study your English"?.

"how many hours a day do you spend studying your English"?
"how many hours a day do you spend to study your English"?.

Which of them is more grammatically correct?.

I have a British English Grammar book that taught me that it is wrong to use "to study" but  my another English Grammar book taught me that it is not. So I am really confused.

Answer

Some verbs take infinitive objects and gerund objects.  Some verbs only take one or the other.  
Ex: I like to study math.  (infinitive object)
Ex: I like studying math.  (gerund object)

Your grammar book should have several pages of explanation and lists of verbs that take both, take an infinitive object, or a gerund object.

Answer

The phrase you need is, "to take/spend time [doing something]".  So the [verb]ing forms are certainly correct.