The mistake almost everyone makes is asking for “a t-shirt with a design on it”. That returns a photo of a shirt — useless, because you can't print a photo of a shirt onto a shirt. What you want is the artwork alone: “Vintage screen-print style graphic of a sun setting behind three mountain ridges, isolated on a flat cream background, centred, no shirt, no mockup”. Say “isolated graphic on a plain background, no garment in frame” in every prompt and you get a file you can actually use.
After that, two clauses do the work. The print technique — “vintage screen print with slight ink texture and a limited three-colour palette”, “bold flat vector illustration with heavy black outlines”, “fine monoline single-weight linework” — decides the entire look and how well it will survive being printed. And the colour count matters commercially: screen printing charges per colour, so “limited three-colour palette of rust, cream and navy” is both a style choice and a cost decision. Every graphic below is an unedited first output generated on BananaBanana.