請問 both 的用法

I need approval from both of you to have access to the library.
我需要你倆的同意才能進圖書館。
to have access to the library = to be allowed to go into the library

看不懂你寫的to grant access for the main entrance要表達的是什麼?

If someone in authority grants you something, or if something is granted to you, you are allowed to have it.
grant應該是授予動詞
此外access通常不會接介系詞for

(1)It is more suitable.It indicates you.Both of your approvals="to show your two approval, regards your two approvals.

(2)It indicates approval.eg:-The both approved two requests for you,agreed to you may be doubled=2x2=4 for you.

(3)grant access means to a grant of large sum of money.

第一句比較恰當。
因為 both of your approvals 清楚地指出 both (A's approval) and (B's approval)

但第二句容易被理解為：
both (approval X and approval Y) from you (a single you).

另一個說法（不敢說更好）：
I need approvals from both of you to ...