What two victories virtually freed New Jersey from British occupation and gave new hope to Washington's men

German Hessian troops were defeated by the continental army of America in both the battles of Princeton and Trenton.

Explanation:

German Hessian troops were already camping in Trenton while General Washington' army camped near the Delaware River near Pennsylvania. After the Christmas night General Washington's army marched towards the camps of the German troops and in the late hours of night time, American army assaulted the German troops who encountered the camps of Washington with surprise and shock.

General Washington' strategy was to reach Trenton and outbreak German camps in the late night and in the darkness. Hessian troops were defeated and the American causalities were very little. Battle of Princeton was also a significant battle which ended up making General Washington victorious in Princeton against The British.