A long time. Hebrew, many days. The campaign in southern Israel lasted for weeks, perhaps even months. But the campaign in northern Palestine must have lasted longer. The vast host which gathered at the waters of Merom was destroyed, but the task of capturing the innumerable cities which dotted that region must have been a protracted one.
We may, with Josephus, infer from Joshua 14:10 that it occupied five years, or perhaps, with other of the ancient Rabbis, seven years, since the wanderings in the wilderness after the rebellion of the Israelites lasted thirty-eight years.