。
We're connected by the red string of fate.
Literal
Fate [possessive-の] red string [with-で] connected [explanatory-んだよ].
運命の赤い糸 ('the red string of fate') is a belief shared across East Asian cultures (originating in Chinese legend) that an invisible red thread connects destined lovers. In Japan it's said to be tied around the little fingers. んだよ adds warm, explanatory conviction — the speaker is stating it as a meaningful truth.