The word "this" refers to collecting money for the believers in Jerusalem. The abstract nouns "relief" and "tribulation" can be stated as verbs. Alternate translation: "We are not asking you to give money to relieve others and make yourselves suffer" (See: [[rc://en/ta/man/jit/figs-explicit]] and [[rc://en/ta/man/jit/figs-abstractnouns]])
"but so that there should be equality" or "but so that there might be equality between others and you." Paul is explaining why he is asking the Corinthians to give money to the believers in Jerusalem.