The regiment, originally 4th Iowa Infantry, dates from the Civil War (or The War Between the States, if you prefer) but I won't go that far back. 168th Infantry was organic to the 34th Infantry Division, one of the division's three regiments of infantry. The regiment was a component of Iowa National Guard prior to being called into Federal service in February 1941 for the one year of active duty for training prescribed by the Selective Service Act of 1940 (the "one year" was extended to "the duration plus six months" upon United States' entry into the war). The regiment was organized at Des Moines, Iowa and moved to Camp Claiborne, near Alexandria, Louisiana about a month later. (From this point the regiment's history pretty well parallels that of the division.) After a little over fourteen months training, the division departed the New York Port of Embarkation 30 April 1942 for duty overseas, arriving in Ireland thirteen days later. Moved to Scotland in August 1942. Equipped, trained and staged in the United Kingdom prior to landing in North Africa. The regiment - with service and support - participated in the Invasion of North Africa, landing near Algiers 8 November 1942 (balance of the division remained in Scotland). The remainder of 34th Infantry Division arrived in North Africa in January 1943. Moved to Italy 21 September 1943 where it served until returning to the United States in October-November 1945. The entire division was inactivated and reverted to state control 3 November 1945 at Camp Patrick Henry, Virginia.
Decorations (regiment only): French Croix de Guerre Streamer, with Palm, embroidered "BELVEDERE". Company B was awarded Presidential Unit Citation for action at Mount Pantano, Italy. Companies E, F & G were awarded Presidential Unit Citation for action at Cervaro, Italy. Mortar Section, Headquarters Company and 1st & 2d Platoons, Company B all were awarded French Croix de Guerre Streamer, with Silver Star, embroidered "France".
Campaign participation credits: Algeria-French Morocco (Invasion), Algeria-French Morocco (Campaign), Tunisia, Naples-Foggia, Anzio, Rome-Arno, North Apennines and Po Valley.
How any of the above applies to your subject depends on his dates of service with the regiment.