how did the creature learn that the cottagers had moved out of their cottage?

When the creature finally summons all of his courage, he knocks upon the De Laceys' door. After a fraught silence, the creature bares his soul to the old man: he tells him that he is a wretched outcast, and that the De Laceys are his only friends in all the world. De Lacey is astonished, but Safie, Felix, and Agatha burst into the cottage before he can reply to the creature's entreaty. The women scream in terror, and Felix, in a "transport of fury," violently beats the creature with his walking stick. The creature, his heart still full of love for the De Laceys, cannot bring himself to retaliate. Instead, he flees the cottage and takes refuge in his hovel.

With the arrival of morning, the creature allows himself to hope that all is not lost: perhaps he can still endear himself to the elder De Lacey, and thereby make peace with his children. When he returns to the cottage, however, he finds it empty. He waits, tortured by anxiety, until Felix finally appears in the company of a strange man. From their conversation, he learns that the De Laceys have determined to leave the cottage out of fear that he (the creature) will return.