She's used to handling this machine.

Literal

She [topic-は] this machine [object-を] handle [for-のに] is-used-to.

~に慣れる ('to get used to X') in its resultant-state form ~に慣れている ('be used to'). The に attaches to a noun normally, but when the target is a verbal action, it gets nominalized first with の: 扱うのに慣れている ('used to handling/operating'). Easy to confuse with the concessive のに ('despite'); here the のに is purposive — 'in the matter of operating.' Once internalized, the pattern is productive: 話すのに慣れている ('used to speaking'), 走るのに慣れている ('used to running').