You need at least a little more information for us.
The 4th Infantry Division never served in Italy. Instead, it campaigned at Normandy, Northern France, Rhineland, Ardennes-Alsace and Central Europe.
If we look up the other possibility, 4th Infantry Regiment, we find it in the Aleutian campaign, and never in Italy.
Your grandfather and I had two things in common: we were both at Camp Wolters, TX, which served as my induction center, July-43; and we both saw service in Italy, where I was in the field artillery, Jan-45/Feb-46.
Do any family members have any mail from him during his stint in Italy? Those old letters are a great resource.