Operation Litani

Though it took the form of an Israeli military incursion into Lebanon, Operation Litani was grounded in the long-running Israeli-Palestinian conflict. From 1968 on, the PLO, Popular Front for the Liberation of Palestine, and other Palestinian groups established a quasi-state in southern Lebanon, using it as a base for raids on northern Israel. This was exacerbated by a massive influx of PLO militants fleeing a defeat in the Jordanian civil war and regrouping in southern Lebanon. Israel responded with damaging attacks against Lebanese villages and PLO bases and an escalating cycle of violence began, eventually culminating in the 1982 Lebanon War and the ejection of the PLO from the country.

Maybe the Israeli really thinks that they can eject Hezbollah from Lebanon, just like they did back then with the PLO. But there is a difference: The PLO was a Palestinian group operating in Lebanon, the Hezbollah is a Lebanese group operating in Lebanon. YMMV
Operation Litani - Wikipedia, the free encyclopedia