Which is correct?
The system administrator’s question was “Will the cost savings of a multi-user environment make up for the difficulty of deploying ____
According to AP style, a question mark is inside quotation marks if that part is the question and outside the quotation marks if the whole sentence is a question. (The same rule applies to exclamation marks and dashes. Periods and commas always go inside quotation marks.)
Grammarbook.com has more information about quotation marks and punctuation.