Can you put some tape inside the box as well so it won't open up?
Why don't you put some tape on the inside too so the box won't tear open?
1) Can you put some tape inside the box as well so it won't open up?
「箱が開かないように中にもテープ貼ってくれない?」
2) Why don't you put some tape on the inside too so the box won't tear open?
「箱が破れないよう中にもテープを貼るのはどう?」
put some tape で「テープを貼る」
inside the box で「箱の中・箱の内側」
ご参考になれば幸いです!