It's difficult to understand the question and the request.
http://www.departments.bucknell.edu/russian/language/prepins.html
За+Ins. This is another multifunctional preposition. Its basic meaning is "behind" and "beyond", but is a busy little fellow that does a lot more than that.
a.
To express the relation of being spatially "behind" or "beyond" something, Russian employs за+Ins if no motion is involved. The same preposition requires the accusative case if it accompanies a verb of motion.
Паша стоит за мной. Pasha is standing behind me.
Его поля за лесом. His fields are beyond the woods.
Даря живёт за городом. Darya lives outside town.
b.
За+Ins is also used to express "for" in two senses.
c.
За+Ins can also mean "at" in the sense of "occupied with".
Я часто застаю их за чтением. I often find them reading.
Он смотрит телевизор за ужином. He watches TV at dinner.
Your question might refer to the B. part, right?
http://www.alphadictionary.com/rusgrammar/for.html
I would say that is "for" = "в течение" "на какой-то период"
1. Я читала книгу три часа. I read the book for three hours. "в течение"
Temporal "for" (Duration of Action) = Accusative case alone
If the phrase meaning "for" indicates of the duration of the action referred to by the verb or the repetition of the action, use the accusative case alone.
2. Temporal "for" (Duration after Action) = на + Accusative
To indicate the duration of a period of time occurring after the completion of the action referred to by the verb, use на plus the accusative case.
Он приехал в Москву на неделю. He came to Moscow for a week. "на какой-то период"
Его послали туда на день. He was sent there for a day.