Situational judgment tests (SJTs) describe work situations and ask which responses are most and least effective, or ask you to rank them. The answer keys are usually built by people who know the job well, and they reward the same habits again and again.
Do what you can yourself before passing a problem on. Tell the right person early about risks, mistakes and missed deadlines, and let people know what happens next. Stay within your authority: don't promise what you can't approve, and never hide an error. Deal with conflict calmly and in private, and stick to facts.
The least effective response is often the one that ignores a problem, hides it, or makes it worse in public. Many SJTs have no strict time limit but are long, so keep a steady pace. There's no trick: answer as a sensible, honest colleague would.