@FutureLawyer99 I'd email graduate recruitment for some clarification on what they mean by research-based case study and if they could elaborate a bit on it but if you don't get the information you're looking for, I'd try to not obsess over the term/structure they've used and instead focus on what they're looking to test you on.
Generally, the point of a case study is to 1) see if you're able to process information swiftly 2) present your findings in a structured and logical manner and 3) justify your reasoning behind the solutions you suggest and/or your ability to decide when to pivot to another solution if you're presented with new information/challenged.
These points are best mastered through practice so try a few scenarios or use do a mock interview here at TCLA or if you're at uni, with your careers counsellor, or with whomever you trust and I think you should be just fine. Wishing you the best!