Which sentence is correct? if i hadn't gone on vacation to washington, i wouldn't have met sam. If i didn't go on vacation to washington, i wouldn't have met sam.

The correct sentence is If I hadn't gone on vacation to Washington, I wouldn't have met Sam. It is a third conditional sentence. It refers to a situation that happened in the past. It means that the person went on vacation and met Sam

The answer is: if I hadn't gone on vacation to Washington, I wouldn't have met Sam.

The conditionals have different forms, in this case if we are using perfect conditional or perfect continuous conditional for the main clause or result is mandatory to use If plus past perfect in the if clause or conditional, this mean s, that the correct sentence should be "If + had" and "would".