It depends on what you want to ask.
"How = kiel?" could have an answer of "with a screwdriver / by turning the top / by bashing it on the surface / by using the zipper / with force / ...".
"With what = per kio?" specifically asks for a tool, and might have an answer of "with a screwdriver / with a saw / ...".
I don't understand this question beginning with "per." Does Esperanto, like English, allow asking questions merely by raising the tone at the end of the sentence? Couldn't (shouldn't?) it be "Ĉu mi povas per kio malfermi ĝin?"
seem strenge that open is malfermi and not that close would be malopen because usually there's a word for the possitive and the word for the negative is mal plus the other word
In the spirit of conceptual translation, and the implied connection between "per" and use ("(use) by") I wrote, "What can I use to open it." It was marked as wrong though.
Yoda? Really? To you maybe. To me, it sounds like formal English - the kind used in formal writing.
P.S. To anybody considering a reply to the effect that this is a made up rule, I agree. :-)
Because you're not opening the container "together with" something or "in the company of" something; you're opening the container "by means of" or "using" something.
English conflates these comitative and instrumental meanings as "with", but Esperanto keeps them separate as kun and per.
That means that Esperanto can't make jokes of the kind "Is it polite to eat sausages with your fingers? -- No; you should eat your fingers separately." which play on the ambiguity of the word "with" ("using" or "together"?).