。
I'm too busy to deal with something like that.
Literal
Busy-[て] that-kind-of place [as-far-as-まで] hand [subject-が] doesn't-reach [emphasis-よ].
手が回らない is an idiom meaning 'can't get to it / too stretched thin.' まで extends the scope — 'all the way to that kind of thing.' そんなところ downplays the matter as minor or peripheral. よ adds assertive emphasis. The whole expression is colloquially natural — a common way to deflect a request.